Which Excel function returns the Z-score for 𝑋 = 72, 𝜇 = 65, 𝜎 = 8? A. =Z.TEST(72, 65, 8) B. =NORM.DIST(72, 65, 8, TRUE) C. =STANDARDIZE(72, 65, 8) D. =NORM.INV(72, 65, 8) E. =NORM.S.INV(0.72)

Which Z-score corresponds to the 95th percentile in a standard normal distribution? A. 1.645 B. 1.96 C. 0.95 D. 2.58 E. 0.645

How many 3-digit numbers can be formed using digits 1 to 5 without repetition?a) 60 b) 125 c) 20 d) 100 e) 10

A question mentions “an average of 4 errors per page” and asks for the probability of getting exactly 2 errors on a page. What type of distribution should you use? A. Normal B. Binomial C. Exponential D. Uniform E. Poisson

Which of the following scenarios is best modelled by a Binomial distribution? A.The time it takes to finish a race B. The number of cars passing a traffic light between 8–9AM C. The number of times a fair coin lands on heads in 10 flips

What is the probability of a continuous random variable taking on an exact value? A. 1 B. Depends on the distribution C. 0 D. 0.5 E. 100%

When can the Poisson distribution approximate the binomial?a) n large, p small b) p = 0.5 c) p close to 1 d) n small, p large e) p = 0

What is the mean of X if X = {1, 2, 3, 4} and P(X) = {0.1, 0.2, 0.3, 0.4}?a) 2.5 b) 3.0 c) 3.1 d) 2.8 e) 2.9

If P(A) = 0.3 and P(B) = 0.6 and A and B are mutually exclusive, what is P(A or B)?a) 0.18 b) 0.9 c) 0.3 d) 0.6 e) 1.2

Which statement best describes 𝑋 ∼ 𝑁 ( 50 , 16 )? A. Mean = 16, SD = 50 B. Mean = 16, Variance = 50 C. Mean = 50, SD = 16 D. Mean = 50, Variance = 16 E. Mean = 4, SD = 50

What is the Poisson distribution used to model?a) Fixed number of trials b) Rare events over time c) Replacement sampling d) Venn diagram logic e) Uniform distributions

If test scores are normally distributed with 𝜇 = 50, 𝜎 = 5, what is the Z-score for a score of 60? A. -2 B. 1.5 C. 2 D. 0 E. 1