Probability and Statistics MCQ Question and Answer
Quiz -3
- XYZ company claims its meat packets remain fresh for five days if refrigerated. An analyst samples 25 packets to test this claim. The average freshness of packets was 4.5 days, with a standard deviation of a day. If the company’s claim is true, find the probability of all selected packets lasting about 4.5 days?
a. 0.04
b. 0.03c. .025
d. 0.01 - Find P (9.8596 < S2 < 79.9236) if a sample of size 10 is taken from a normal population having variance 42.5.
a. 0.75
b. 0.95
c. 0.5
d. 0.5Sampling distribution of the mean refers to:
- a. The distribution of sample means taken from different populations
b. The distribution of sample means taken from different samples of the same size from a population
c. The distribution of individual data points in a population
d. The distribution of means from a single sample - In statistics, parameters are:
a. Descriptive characteristics of the sample
b. Descriptive characteristics of the population
c. Measures of central tendency within a sample
d. Measures of variability within a sample
- If χ2α = 23.589 for a sample of size 10, then find α?
a. 0.050
b. 0.025
c. 0.005
d. 0.010 - The number of all possible samples from a population containing 10 items from which 2 items are selected at random without replacement
a. 20
b. 90
c. 45
d. 10 - Pulse rates of adult men are approximately normal with a mean of 70 and a standard deviation of 8. Which choice correctly describes how to find the proportion of men that have a pulse rate greater than 78?
a. Find the area to the right of z =1 under a standard normal curve.
b. Find the area to the right of z = −1 under a standard normal curve
c. Find the area to the left of z = 1 under a standard normal curve.
d. Find the area between z = −1 and z = 1 under a standard normal curve. - What is the name of the probability of making a Type I error?
a. Level of significance
b. Margin of error
c. Power of the test
d. Confidence interval
- What is the name of the alternative hypothesis that specifies that the population mean is not equal to the value assumed under the null hypothesis?
a. Two-sided alternative
b. Two-tailed alternative
c. One-sided alternative
d. One-tailed alternative - Suppose the p-value for a test is .02. Which of the following is true?
a. We will reject H0 at alpha equals 0.01, 0.05, and 0.10
b. We will not reject H0 at alpha = .05
c. We will reject H0 at alpha = 0.05
d. We will reject H0 at alpha = .01 - When σ is known, the hypothesis about population mean is tested by _____
a. F – test
b. t – test
c. Chi – Square test
d. Z – test - If -t0.05 = tα then α is……………………….
a. 0.05
b. 0.95
c. -0.05
d. -0.95
- If the size of the sample is 25 drawn from the normal population and maximum error with 95% confidence is 0.1 the S.D of the sample is
a. 0.255
b. 2.12
c. 2.55
d. 0.025 - The Central Limit Theorem states that:
a. As the sample size increases, the sampling distribution of the sample mean approaches a normal distribution
b. The standard deviation of a sample will be equal to the standard deviation of the population
c. The mean of a sample will be equal to the mean of the population
d. The population and sample will have the same shape of distribution - The mean and standard deviation of marks in an examination are 74 and 12 respectively. find the z-score corresponding to marks 74
a. -0.75
b. 1
c. 0
d. 1.5 - A random sample of size 169 was taken from population whose variance is 25 and mean is 50 the 99% C.I. is
a. (48.5, 50.25)
b. (48, 50)
c. (49.25, 50.75)
d. (49, 51)
- Find the probability that the variance of a random sample of size 5 from a normal population with σ = 12 will exceed 180?
a. 0.3
b. 0.2
c. 0.4
d. 0.1 - Suppose for a statistical inferences about the mean, u, of a normal population with standard deviation σ = 2 with a random sample of size n = 49, from this population give a sample mean = 4.5. Then the standard error of £ is
A. 0.0816
B. 0.0408
C. 0.2857
D. 0.5714 -
In one of the survey, 27% of Indian will do 30 minutes of exercise per day. If you take a simple random sample of 25 Indians and let p = the proportion in the sample who will do 30 minutes of exercise per day, then the mean and standard deviation of the sampling distribution of p are
A. 0.30, 0.1039
B. 0.30, 0.0888
C. 0.27, 0.0079
D. 0.27, 0.0888 -
For the confidence level of 99%, the parameter zα/2 for the normalized distribution is
A. 1.645
B. 1.960
C. 2.326
D. 2.576
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Quiz -2
- The mean and variance of the Poisson distribution is given by
a. e
b. Parameter
c. Constant
d. Standard deviation - Let X be uniformly distributed in -3£X£3 then mean m=________
a. 5
b. 4
c. 6
d. 3 - When α=1 gamma distribution results in
a. Exponential distribution
b. Beta distribution
c. Normal distribution
d. Uniform distribution - The mean , median , mode of a normal distribution are :
a. 1
b. 0.5
c. ∞
d. 0 - Increasing the sample size of an opinion poll will reduce the
a. variability of the estimates made from the poll data
b. Variability of opinions in the sample
c. bias of the estimates made from the poll data
d. variability of opinions in the population - A sample of 25 are selected from a population with mean 40 and standard deviation 7.5.
a. The mean of the sampling distribution of sample means is 7.5
b. The mean of the sampling distribution of sample means is 8
c. The mean of the sampling distribution of sample means is 40
d. None of the above - Let X and Y are random variables such that the point (1,2) occurs with probability 1/4 , (1,3) with probability 1/2 , (2,3) and (3,1) with probability 1/8 each . Calculate P(Y=2/X=1 ).
a. 5/8
b. 1/3
c. 1/4
d. 3/4 - When a coin is tossed 6 times the probability of getting 4 heads is
A. 13/64
B. 16/64
C. 15/64
D. 9/64 - The expected value of the random variable x and standard deviation for the discrete distribution
x | 8 12 16 20 24
—————————————–
p(x) | 1/8 1/6 3/8 1/4 1/12
A. 8 & 2√5
B. 16 & 2√5
C. 8 & 5√2
D. 16 & 5√2 - For a discrete distribution cumulative distribution is defined as
A. F(x) = p(X ≤ x)
B. F(x) = p(x > x)
C. F(x) = p(x = x)
D. Any of the above - For the normal distribution with µ = 28 and o² = 100, then value of Z με corresponding to X=30 is
a. Z=0.1
b. Z=0.2
c. Z=0.3
d. None of these - The & value and mean respectively for the distribution
x | 1 2 3 4
—————————————–
p(x) | k/2 k/4 k/6 k/8A. 24/25 & 46/25
B. 24/25 & 44/25
C. 22/25 & 48/25
D. 24/25 & 48/25 - Let U and v are two identically distributed independent random variables. Suppose U E {0,1,2) with P(U = 0) = 1/2, P(U = 1) = P(U = 2) = 1/4,Similarly v € {0,1,2) with P(V = 0) = 1/2, P (V = 1) = P(V = 2) = 1/4,Then find P(U+V=2/U – V = 0).
a. 1/16
b. 0
c. 1/6
d. 1 - The random variables X and Y have the joint probability density function
f(x, y)={1/6,0<x<2,0<y<3
0,otherwise
The marginal pdf of X is
a. f(x) = ½, 0 < x <3
b. f(x) = ½, 0 < x <6
c. f(x) = 1/2, 0 < x <2
d. f(x) = 1/2, 2<x<3 - Consider following joint probability function
Find Var(X).
a. 0.4768
b. 0.6784
c. None of these
d. 0.8647 - If the joint probability density function of the random variable( x, y ) is given by f(x,y) = 2, for 0 ≤x≤ y ≤1 then the marginal pdf of y, fy(y), is
A. 2y for 0 ≤ y ≤1
B. 2y for 0 ≤ x ≤ y ≤1
C. 2y for 0 ≤ x ≤1
D. y for 0 ≤ y ≤1 - Consider the table below Which classifies responses for the variable’s social life rating and gender. What is the conditional probability of of females with a “Excellent” social life rating?
a 0.52
b. 0.18
c. 0.21
d. 0.34 - If X is a Poisson variate with P(0) = 0.2725, then P(1)= ……………………………
a. 0.3543
b. 0.0001
c. 0.6457
d. 0.9999 - The number of arrivals per hour at an automatic teller machine is Poisson distributed with a mean of 3.5 arrivals per hour. What is the probability that more than 3 arrivals occur in an hour?
a. 0.3209
b. 0.4633
c. 0.6791
d. 0.5367 - If a random variable has a Poisson distribution such that P(1) = P(2), then the mean of the distribution is ………………………………………
a. 2/e
b. E
c. 2
d. 2e
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Quiz -1
- Baye’s theorem is useful in
a. Computing sequential probabilities
b. Revising prior probabilities
c. Computing conditional probabilities
d. Marginal probabilities - Let U and V are two events with U is subset of V and P(V)>0 then which of the following options is/are correct
a. P(UV)<P(U)
b. P(UV)>=P(U)
c. P(UV)=P(U)/P(V)
d. P(UV)=P(U) - A company manufactures electronic components for laptops. Among them 5% failed in final inspection. If 240 components are inspected in one day, then what is the expected number that pass in one day?
a 226
b. 225
c. 220
d. 228 - In a town on an average 10 accidents occur in a span of 50 days. Find the probability that there will be at least 3 accidents in a day
a. 0.1200
b. 0.0012
c. 0.002
d. 0.012 - size n is —– and V(X) is ——
a. n = 25 and V(X) = 4
b. n = 15 and V(x) = 4
c. n = 30 and V(X) = 4.8
d. n = 25 and V(X) = 5 - Let X follows binomial distribution and given P(X=0)=16/81,n=4, then P(X=1)=?
a. 32/81
b. 27/81
c. 1/81
d. 8/81 - A fair die is rolled twice. The probability that an odd number will follow an even number is
a. 1/6
b. 1/4
c. 1/2
d. 1/3 - If mean is 2 and variance is 1 for Binomial distribution then P(X1) is
a. 7/16
b. 8/3
c. 3/16
d. 5/16 - An unbiased coin is tossed infinitely. Then the probability that fourth head appears at the 10th toss is
a. 120/512
b. 48/512
c. 84/1024
d. 210/1024 - The probability of obtaining an even prime number on each die, when a pair of dice is rolled is
a. 1/36
b. 5/36
c. 2/5
d. 1/12 - Bag I contain 7 tickets numbered from 1 to 7, and Bag II contains 6 tickets numbered from 1 to 6. A bag is selected at random and a ticket is drawn randomly. If the number on ticket is odd then the probability of the ticket came from bag II is __________
a. 8/15
b. 7/15
c. None of these
d. 9/15 - If the probability of defective items made by a factory is 0.004, then the probability that less than 2 items are defective in the sample of 1000 items is
a. 4e^(-4)
b. 4e^(-1/4)
c. 5e^(-4)
d. 4e^(-6) - A company manufactures electronic components for laptops. Among them 5% failed in final inspection. If 240 components are inspected in one day, then what is the expected number that pass in one day?
a. 228
b. 225
c. 220
d. 226 - Three companies A, B and C supply 25%, 35% and 40% of the notebooks to a school. Past experience shows that 5%, 4% and 2% of the notebooks produced by these companies are defective. what is the probability that it is found to be defective if the notebook was supplied by A?
a. 0.02
b. 0.05
c. 0.04
d. none of the above - A bag contains 6 balls and 4 marbles. Out of them two are selected randomly without replacement. What is the probability to get a ball in the first draw and a marble in the second draw?
a. 3/15
b. 1/15
c. 2/15
d. 4/15 - An experiment consists of two events A and B where P(A)=0.3 and P(B)= 0.6. what is the probability that event A or event B will occur if A and B are mutually exclusive?
a. 1
b. 0.6
c. 0.8
d. 0.9 - P(X) 0.05 0.17 0.43 0.35 is
a. 1.69
b. 2.44
c. 2.85
d. 1.56 - When will an event A be independent of itself
a. If and only if P(A)=1
b. If and only if P(A)=0
c. If and only if P(A)=0 or P(A)=1A.
d. Always - In an examination paper, there are two sets each containing 4 questions. A candidate is required to attempt 5 questions but not more than 3 questions from any set. In how many ways can 5 questions be selected?
a. 48
b. 24
c. 20
d. 28 -
A letter is chosen at random from the word “ASSASSINATION”. Find the probability that the letter is not a vowel
A. 2/5
B. 7/13
c. 6/13
D. 5/13
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