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Question paper · SSC CGL

SSC CGL 2017 Tier II — Statistics — 22 February 2018

22 February 2018 · 10:30 AM–12:30 PM86 of the paper’s 100 questions1 per correct answer

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14 questions of the original paper are not included: those that need a figure or formatting we cannot show, that have no answer in the response sheet, or that we could not check against a second copy of the paper.

Questions from the Staff Selection Commission’s paper of 22 February 2018, 10:30 AM–12:30 PM. Each question’s answer is under it, hidden until you open it, and the full answer key is at the end. Take the paper as a timed practice test to be scored.

Statistics

1. For the mid values 30, 39, 48, 57 and 66 the second class of the distribution is ________.
- (a) 34 - 44
- (b) 34.5 - 43.5
- (c) 33.5 - 44.5
- (d) 34 - 45
Show answer
Answer: (b)
4. In a pie chart depicting total expenses of a company for the year 2016, raw material had a central angle of 45o. If total expenses were Rs 504 Lakhs, what were the company's expense on raw materials (in Rs lakhs)?
- (a) 45
- (b) 112
- (c) 63
- (d) 72
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Answer: (c)
8. Find the harmonic mean of 3, 6 and 10.
- (a) 6.33
- (b) 5
- (c) 5.6
- (d) 4.5
Show answer
Answer: (b)
10. Calculate the median using the following data. Lower class boundary of the median class = 40 Total frequency = 120 Frequency of the median class = 35 Less than cumulative frequency of the post median class = 37 Class width = 20
- (a) 48.23
- (b) 49.14
- (c) 54.23
- (d) 53.14
Show answer
Answer: (d)
13. Compute the standard deviation of the following numbers: 5, 6, 4 and 2
- (a) 1.7
- (b) 2.7
- (c) 1.2
- (d) 2.2
Show answer
Answer: (a)
14. Calculate the standard deviation if the mean of a certain set of observations is 20 and the mean of the squares of the same observations is 500.
- (a) 5
- (b) 20
- (c) 10
- (d) 25
Show answer
Answer: (c)
15. Calculate the coefficient of range for the following set of data. 3, 6, 6, 8, 9 and 12
- (a) 22.2
- (b) 44.4
- (c) 50
- (d) 60
Show answer
Answer: (d)
16. The mean and variance of the marks of Division 1 which has 60 students is 45 and 4 respectively and the mean and variance of the marks of Division 2 which has 40 students is 55 and 9 respectively. What will be the variance of the marks of the two divisions combined?
- (a) 30
- (b) 20
- (c) 10
- (d) 40
Show answer
Answer: (a)
17. If the mean of a certain set of data is 16 and variance is 4 then find the coefficient of variance.
- (a) 25
- (b) 12.5
- (c) 10
- (d) 20
Show answer
Answer: (b)
18. If a set of points represent probability density, then the third central moment is the ______________.
- (a) skewness
- (b) kurtosis
- (c) mean
- (d) variance
Show answer
Answer: (a)
19. Which formula represents the 2nd moment around the mean?
- (a) Σ(xi – μx)2
- (b) √Σ(xi – μx)2
- (c) Σ(xi2 – μx2)
- (d) √ Σ(xi2 – μx2)
Show answer
Answer: (a)
20. Calculate skewness using Bowley's formula given lower quartile, upper quartile and median values of a data set are 16, 40 and 24.
- (a) 0.33
- (b) 0.44
- (c) 0.55
- (d) 0.67
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Answer: (a)
21. What is the mean of a data if its Pearson's coefficient of skewness is 0.25, standard deviation is 6 and mode is 18?
- (a) 16.5
- (b) 10.5
- (c) 21.5
- (d) 19.5
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Answer: (d)
22. Which condition has to be met to say that a series has positive skewness?
- (a) Mode > Mean > Median
- (b) Median > Mode > Mean
- (c) Mode > Median > Mean
- (d) Mean > Median > Mode
Show answer
Answer: (d)
23. The kurtosis of any univariate normal distribution is ________.
- (a) 2
- (b) 3
- (c) 1
- (d) 0
Show answer
Answer: (b)
24. Characteristics of a leptokurtic distribution are ____________________.
- (a) 1)Positive excess kurtosis, 2) Slender in shape and 3)Fatter tails
- (b) 1)Negative excess kurtosis, 2) Slender in shape and 3)Fatter tails
- (c) 1)Positive excess kurtosis, 2) Thicker in shape and 3)Thinner tails
- (d) 1)Negative excess kurtosis, 2) Thicker in shape and 3)Thinner tails
Show answer
Answer: (a)
25. Coefficient of Kurtosis β2 = ____________, where μ2 and μ4 are the second and fourth moments about mean.
- (a) μ2/μ42
- (b) μ42/μ2
- (c) μ4/μ22
- (d) μ22/μ4
Show answer
Answer: (c)
26. Find the coefficient of correlation if the two regression coefficients are 0.5 and 4.5.
- (a) 1.5
- (b) 2.5
- (c) 3.5
- (d) 2.25
Show answer
Answer: (a)
27. Pearson's correlation coefficient = _________________. (S represents standard deviation)
- (a) (Sx.Sy)/Covariance(x,y)
- (b) Covariance2(x,y)/(Sx.Sy)
- (c) (Sx.Sy)2/Covariance(x,y)
- (d) Covariance(x,y)/(Sx.Sy)
Show answer
Answer: (d)
28. The range of values that coefficient of correlation can take are _____________.
- (a) 0 ≤ r ≤ +1
- (b) -1 < r < +1
- (c) 0 < r < +1
- (d) -1 ≤ r ≤ +1
Show answer
Answer: (d)
29. Spearman's rank correlation coefficient is given by _____________.
- (a) 1 + 6∑di2/[n(n2-1)]
- (b) 1 - 6∑di/[n(n2-1)]
- (c) 1 - 6∑di2/[n(n2-1)]
- (d) 1 + 6∑di/[n(n2-1)]
Show answer
Answer: (c)
30. If Coefficient of correlation r = 0.5 then coefficient of non-determination is __________.
- (a) 0.5
- (b) 0.25
- (c) 1
- (d) 0.75
Show answer
Answer: (d)
31. If x = 3u + 1 and y = 4v + 2 and the regression coefficient between u and v is 1.2, then find regression coefficient between x and y?
- (a) 0.8
- (b) 1
- (c) 0.9
- (d) 1.5
Show answer
Answer: (c)
32. Calculate the correlation coefficient between the following values : x: 3, 5, 1, 7, 5 y: 4, 3, 0, 8, 2
- (a) 0.9
- (b) 0.8
- (c) 0.7
- (d) 0.6
Show answer
Answer: (b)
33. If the sum of the squares of difference of ranks of 6 candidates in two criteria is 21, the rank correlation coefficient is __________.
- (a) 0.5
- (b) 0.6
- (c) 0.4
- (d) 0.7
Show answer
Answer: (c)
34. If 4y = 15 + 6x is the regression line of y on x, and coefficient of correlation between x and y is 0.9, then regression coefficient of x on y is equal to _______.
- (a) 0.54
- (b) 0.45
- (c) 0.81
- (d) 0.72
Show answer
Answer: (a)
35. Find regression coefficient of y on x (byx) if correlation coefficient between x and y values is 0.75 and standard deviation of x and y are 5 and 6.4 respectively.
- (a) 0.96
- (b) 0.59
- (c) 1.04
- (d) 1.7
Show answer
Answer: (a)
36. If a box contains 4 red balls and 6 blue balls then what is the probability of picking 2 balls of the same colour?
- (a) 8/15
- (b) 12/25
- (c) 13/25
- (d) 7/15
Show answer
Answer: (d)
37. A doctor finds of all patients that visits his clinic the probability that a patient is alcoholic given that the patient has liver disease is 0.08. The probability that a patient is alcoholic is 0.06 and the probability that a patient has liver disease is 0.12. Find the probability that a patient has liver disease given that he or she is alcoholic?
- (a) 0.04
- (b) 0.09
- (c) 0.16
- (d) 0.24
Show answer
Answer: (c)
38. What is the probability that a number selected randomly from 1 to 500 is a multiple of 3 or 7?
- (a) 0.428
- (b) 0.474
- (c) 0.512
- (d) 0.576
Show answer
Answer: (a)
39. If P(A) = 2/3 and P(B) = 5/8 and find probability of only B occurring if probability of only A occurring is 1/6?
- (a) 1/8
- (b) 1/9
- (c) 1/6
- (d) 2/9
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Answer: (a)
40. Find P(A'/B'), given P(A) = 3/4, P(B) = 9/20 and P(A∩B) = 1/4? P(A'/ B')
- (a) 1/20
- (b) 1/9
- (c) 1/11
- (d) 1/12
Show answer
Answer: (c)
41. A and B are independent events. The odds in favour of A and B are 1:1 and 3:2 respectively. Find the probability that only one of the two events occurs?
- (a) 0.6
- (b) 0.7
- (c) 0.8
- (d) 0.5
Show answer
Answer: (d)
43. If 3 dice are thrown what is the probability of getting same digits on atleast two dices?
- (a) 1/36
- (b) 7/36
- (c) 27/216
- (d) 1/6
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Answer: (d)
44. In a family of three children what is probability that the third child is a girl given that the other two are also girls?
- (a) 1/3
- (b) 2/3
- (c) 1/4
- (d) 1/6
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Answer: (c)
45. A, B and C are three mutually exclusive and exhaustive events. P(A) = 2P(B) = 6P[C). Find P(B).
- (a) 0.1
- (b) 0.3
- (c) 0.6
- (d) 0.4
Show answer
Answer: (b)
47. In a box of 100 bulbs 30 are defective. What is the probability of getting more than 2 defective bulbs if 5 are chosen randomly from the box?
- (a) 0.124
- (b) 0.213
- (c) 0.264
- (d) 0.163
Show answer
Answer: (d)
48. The mean and variance of a binomial distribution are 5 and 4 respectively. What is the probability of success?
- (a) 0.3
- (b) 0.2
- (c) 0.4
- (d) 0.1
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Answer: (b)
49. If the mean of a Poisson distribution is 9 then its variance is equal to ________.
- (a) 3
- (b) 9
- (c) 6
- (d) 81
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Answer: (b)
50. Find the mean of x if x is a Poisson variate satisfying the condition P(3) = P(4)?
- (a) 2
- (b) 8
- (c) 4
- (d) 16
Show answer
Answer: (c)
51. For a standard normal distribution P(-1 < z < 1) = __________
- (a) 0.68
- (b) 0.34
- (c) 0.99
- (d) 0.49
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Answer: (a)
52. If x follows normal distribution with mean = 20 and variance = 25. What is P(x ≥ 25)? Given P(z ≤ 1) = 0.841, P(z ≤ 2) = 0.977
- (a) 0.023
- (b) 0.16
- (c) 0.32
- (d) 0.046
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Answer: (b)
53. 10% of people in a village are afflicted with a viral disease. What size of sample should be taken to ensure that error of estimation of the proportion is not more than 5% with 95% confidence?
- (a) 138
- (b) 238
- (c) 38
- (d) 338
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Answer: (a)
54. A random sample of 100 articles from a large batch of articles contains 10 defective articles. What is the standard error of estimation of the sample proportion?
- (a) 0.02
- (b) 0.01
- (c) 0.04
- (d) 0.03
Show answer
Answer: (d)
55. A statistician estimated that the standard deviation of her measurements is 2 cm. What should be the size of the sample in order to be 99% confident that the error of her estimates of mean does not exceed 0.43 cm? (z* = 2.58, for 99% confidence level)
- (a) 144
- (b) 121
- (c) 169
- (d) 196
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Answer: (a)
57. A random sample of 2 items is picked out from a population of 15 items. The number of all such samples is ________.
- (a) 105
- (b) 60
- (c) 210
- (d) 90
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Answer: (a)
58. The average length of a sample of 50 leaves measured by a botanist was 40 mm with a standard deviation of 21 mm. Assuming normal deviation find the limits which have a 95% chance of including the expected length of the leaf.
- (a) 42.35 - 37.65
- (b) 34.12 - 45.88
- (c) 43.12 - 36.88
- (d) 44.58 - 35.42
Show answer
Answer: (b)
59. The 95% confidence level limits to a population mean are 94.12 - 105.88. Find population standard deviation if sample size is 100.
- (a) 15
- (b) 30
- (c) 45
- (d) 60
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Answer: (b)
60. In a particular study if the sample size was 50, then standard error was 8 units. How much would be the standard error if sample size was increased to 200?
- (a) 4
- (b) 2
- (c) 16
- (d) 8
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Answer: (a)
61. A random sample of 200 articles taken from a large batch of articles contains 15 defective articles. What is the estimate of the sample proportion of defective articles?
- (a) 0.186
- (b) 0.054
- (c) 0.0186
- (d) 0.54
Show answer
Answer: (c)
62. A factory manufactures 10,000 bolts per day. From a sample of 500 bolts, 4% were of unacceptable quality. Estimate the interval of number of bolts that would be of unacceptable quality produced per day at 95% confidence.
- (a) (313, 487)
- (b) (305, 495)
- (c) (328, 472)
- (d) (233, 567)
Show answer
Answer: (d)
63. The mean pay of 15 H1-B visa holders was found to be Rs 65 lakhs/yr with a standard deviation of Rs 6 lakhs. What are the 99% confidence limits (in Rs lakhs) for the mean pay of the population of H1-B visa holders assuming it to be normal? (The upper 0.5% of t-distribution with 14 degrees of freedom is 2.98)
- (a) (61.88 , 68.12)
- (b) (60.22 , 69.77)
- (c) (62.55 , 67.45)
- (d) (59.33 , 70.67)
Show answer
Answer: (b)
64. The standard error of the mean decreases if the population standard deviation ____________________________.
- (a) increases or if sample size increases
- (b) decreases or if sample size increases
- (c) decreases or if sample size decreases
- (d) increases or if sample size decreases
Show answer
Answer: (b)
65. A confidence interval increases in width as the __________________.
- (a) sample size is increased
- (b) degrees of freedom is increased
- (c) level of confidence increases
- (d) sample standard deviation is decreased
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Answer: (c)
66. What is the value of the z-score for x = 125 if population mean and variance are 121 and 4 respectively.
- (a) 2
- (b) 1
- (c) -2
- (d) -1
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Answer: (a)
67. In statistical hypothesis testing, a type I error is the _______________________________ a false null hypothesis
- (a) incorrectly retaining of a true null hypothesis, while a type II error is incorrectly retaining
- (b) incorrect rejection of a true null hypothesis, while a type II error is incorrectly retaining
- (c) incorrect rejection of a true null hypothesis, while a type II error is incorrect rejection
- (d) incorrectly retaining of a true null hypothesis, while a type II error is incorrect rejection
Show answer
Answer: (b)
68. If, Sample from Population #1: 3,5,8 Sample from Population #2: 2,4,8 Sample from Population #3: 3,6,7 Then what is the number of degrees of freedom of treatment?
- (a) 3
- (b) 1
- (c) 4
- (d) 2
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Answer: (d)
69. If we have to test if there’s a difference between two groups of patients from different hospitals trying two different therapies, then we need to use ___________.
- (a) Two way ANOVA without replication
- (b) One way ANOVA with replication
- (c) Two way ANOVA with replication
- (d) One way ANOVA without replication
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Answer: (c)
70. If confidence level is 90% then two tailed alpha would be ________ %.
- (a) 10
- (b) 45
- (c) 2.5
- (d) 5
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Answer: (d)
71. The smaller the alpha level, the ____________________ the null hypothesis.
- (a) greater the area where you would reject
- (b) smaller the area where you would reject
- (c) smaller the area where you would accept
- (d) greater the area where you would accept
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Answer: (b)
72. The mean square of error denoted as MSE = _____________. Where SSE is the sum of squares of error, n is number of data points and m is number of samples.
- (a) SSE/(n - m - 2)
- (b) SSE/(n + m)
- (c) SSE/(n + m - 2)
- (d) SSE/(n - m)
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Answer: (d)
73. The mean square for treatment is 9. The mean square for error is 4. Calculate the F-statistic.
- (a) 1.5
- (b) 2.25
- (c) 0.44
- (d) 0.66
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Answer: (b)
74. An ANOVA procedure is used for data that was obtained from four sample groups each comprised of five observations. The degrees of freedom dF1 and dF2 for the critical value of F are _________ respectively.
- (a) 3 and 16
- (b) 3 and 19
- (c) 4 and 16
- (d) 4 and 19
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Answer: (a)
75. When an analysis of variance is performed on samples drawn from k populations, the mean square between treatments (MSTR) is __________________. (Where SSTR is treatment sum of squares and SST is total sum of squares.)
- (a) SSTR/(k - 1)
- (b) SST/(k - 1)
- (c) SSTR/(k+1)
- (d) SST/k
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Answer: (a)
76. Convert the annual trend equation Y = a + bX into monthly trend equation.
- (a) Y = a/12 + (b/12)X
- (b) Y = 12a + bX
- (c) Y = a/12 + (b/144)X
- (d) Y = a + 12bX
Show answer
Answer: (c)
77. What is the shape of the second degree trend equation?
- (a) Hyperbolic
- (b) Parabolic
- (c) Exponential
- (d) Sinusoidal
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Answer: (b)
78. If the sales (Y) Vs time (X) trendline with 2010 as origin is Y = 16.25 + 1.25X, then what will be the trendline with 2015 as origin?
- (a) Y = 10 + 1.25X
- (b) Y = 22.5 + 6.25X
- (c) Y = 10 + 6.25X
- (d) Y = 22.5 + 1.25X
Show answer
Answer: (d)
79. If the sales (Y) trend is captured by the equation Y = 500 + 20t - t2 then the maximum sales will be achieved when the time t = ________ years .
- (a) 20
- (b) 5
- (c) 15
- (d) 10
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Answer: (d)
80. Y = 500 + 0.75 t - 2.5 t2 represents the trend for output of a copper mine with 2010 as origin. Unit of Y is tonnes and unit of t is year. What will be the mine's copper output (in tonnes) in the year 2020?
- (a) 185.5
- (b) 346.5
- (c) 257.5
- (d) 742.5
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Answer: (c)
81. The fitted annual sales trend is Yt = 180 e0.2t. (Where t is in years and Y is in Rs lakhs) On average, sales are ___________absolute amount each year.
- (a) rising by a declining
- (b) falling by a declining
- (c) falling by an increasing
- (d) rising by an increasing
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Answer: (d)
82. A pattern of variation of a time series that repeats every year is called _____________.
- (a) Cyclical
- (b) Trend
- (c) Hyperbolic
- (d) Seasonal
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Answer: (d)
84. The linear trend equation developed for the annual sales Y (in Rs lakhs) of ABC Manufacturing Company is Y = 500 + 6t, where t is in years. By how much are sales increasing per year?
- (a) Rs 6,00,000 6,00,000
- (b) 6 percent
- (c) 6 times the number of years
- (d) in multiples of 6
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Answer: (a)
85. For the linear trend equation Y = a + bt, which symbol represents the average change in the dependent variable for each unit change in time?
- (a) a
- (b) t
- (c) Y
- (d) b
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Answer: (d)
86. If the trend equation to forecast demand Y (in Rs lakhs) for the required month (t) is Y = 100 + 20t - 5t2. What is the seasonally adjusted demand forecast for month 3 for which the corresponding seasonal index is 1.25?
- (a) 143.75
- (b) 115
- (c) 92
- (d) 123.25
Show answer
Answer: (a)
87. Y = 100 - 0.4 t - t2 represents the trend for sales of movie tickets in a multiplex with day before release as origin. Unit of Y is in Rs thousand and unit of t is days. Sales for day 3 are ____________ than sales of day 1.
- (a) 8.9% greater
- (b) 9.8% lesser
- (c) 8.9% lesser
- (d) 9.8% greater
Show answer
Answer: (c)
88. If the quarterly trend equation is given as Y = a + bX, then the annual trend equation will be ________________.
- (a) Y = 4a + 4bX
- (b) Y = 4a + bX
- (c) Y = a + 4bX
- (d) Y = 4a + 48bX
Show answer
Answer: (d)
89. The last period’s sales forecast was Rs 100 lakhs and demand was Rs 90 lakhs. What is the simple exponential smoothing sales forecast (in Rs lakhs) with alpha of 0.4 for the next period?
- (a) 94
- (b) 106
- (c) 96
- (d) 104
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Answer: (c)
90. If the trendline with 2016 as origin is Y = 125 - 3t -2t2, then what will be the trendline with 2014 as origin?
- (a) Y = 127 + 5t -2t2
- (b) Y = 123 + 5t -2t2
- (c) Y = 125 + 7t -2t2
- (d) Y = 127 + 7t -2t2
Show answer
Answer: (b)
92. From the prices and quantities of the base and current year Laspeyres and Bowley Price Indices were calculated as 124 and 130 respectively. Find the Paasche price index for the same data.
- (a) 127
- (b) 136
- (c) 118
- (d) 121
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Answer: (b)
93. Paasche Quantity Index is given by the formula ______________.
- (a) (∑QnPo)/(∑QoPo)
- (b) (∑QnPn)/(∑QoPn)
- (c) (∑QoPn)/(∑QoPn)
- (d) (∑QnPn)/(∑QnPo)
Show answer
Answer: (b)
94. The index number for the price of diesel in 2015 was 125 and in 2016, it was 140, on a base year of 2011. What is the percent increase in price of diesel from 2015 to 2016?
- (a) 25
- (b) 40
- (c) 12
- (d) 15
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Answer: (c)
95. A worker earned Rs 15,000 per month in 2015, when the Consumer Price Index was 250. If the base period is 2000, what are his earnings per month in 2015 in terms of value of Rs. in the year 2000?
- (a) Rs 37,500
- (b) Rs 6,000
- (c) Rs 10,000
- (d) Rs 27,500
Show answer
Answer: (b)
96. The price index in 2016 is 116 using 2011 as base year. What will be 2011 price index if base year is changed to 2016?
- (a) 134.5
- (b) 86.2
- (c) 84
- (d) 132
Show answer
Answer: (b)
97. The Fisher's Index _____________________.
- (a) satisfies neither the Time Reversal Test nor the Factor Reversal Test
- (b) satisfies the Time Reversal Test but not the Factor Reversal Test
- (c) satisfies both the Time Reversal Test as well as the Factor Reversal Test
- (d) satisfies the Factor Reversal Test but not the Time Reversal Test
Show answer
Answer: (c)
98. Calculate Fisher's Price Index (in %) using the following data: ∑QoPn = 2700, ∑QnPn= 2250, ∑QoPo= 2750 and ∑QnPo= 2100 ΣQoPn = 2700, ΣQnPn = 2250, ΣQnPo = 2100
- (a) 157.1
- (b) 63.6
- (c) 102.5
- (d) 95
Show answer
Answer: (c)
99. Find the Value Index (in %) using the following data: ∑QoPn = 2500, ∑QnPn = 2750, ∑QoPo = 2250 and ∑QnPo = 2000. ΣQoPn = 2500, ΣQnPn = 2750, ΣQnPo = 2000
- (a) 122.2
- (b) 125
- (c) 112.5
- (d) 137.5
Show answer
Answer: (a)

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Answer key

Answer key as marked in the Staff Selection Commission’s response sheet. “—” means the sheet did not show it clearly.

Statistics

Q 1: (b)
Q 4: (c)
Q 8: (b)
Q 10: (d)
Q 13: (a)
Q 14: (c)
Q 15: (d)
Q 16: (a)
Q 17: (b)
Q 18: (a)
Q 19: (a)
Q 20: (a)
Q 21: (d)
Q 22: (d)
Q 23: (b)
Q 24: (a)
Q 25: (c)
Q 26: (a)
Q 27: (d)
Q 28: (d)
Q 29: (c)
Q 30: (d)
Q 31: (c)
Q 32: (b)
Q 33: (c)
Q 34: (a)
Q 35: (a)
Q 36: (d)
Q 37: (c)
Q 38: (a)
Q 39: (a)
Q 40: (c)
Q 41: (d)
Q 43: (d)
Q 44: (c)
Q 45: (b)
Q 47: (d)
Q 48: (b)
Q 49: (b)
Q 50: (c)
Q 51: (a)
Q 52: (b)
Q 53: (a)
Q 54: (d)
Q 55: (a)
Q 57: (a)
Q 58: (b)
Q 59: (b)
Q 60: (a)
Q 61: (c)
Q 62: (d)
Q 63: (b)
Q 64: (b)
Q 65: (c)
Q 66: (a)
Q 67: (b)
Q 68: (d)
Q 69: (c)
Q 70: (d)
Q 71: (b)
Q 72: (d)
Q 73: (b)
Q 74: (a)
Q 75: (a)
Q 76: (c)
Q 77: (b)
Q 78: (d)
Q 79: (d)
Q 80: (c)
Q 81: (d)
Q 82: (d)
Q 84: (a)
Q 85: (d)
Q 86: (a)
Q 87: (c)
Q 88: (d)
Q 89: (c)
Q 90: (b)
Q 92: (b)
Q 93: (b)
Q 94: (c)
Q 95: (b)
Q 96: (b)
Q 97: (c)
Q 98: (c)
Q 99: (a)