Question

The grades on the last science exam had a mean of 89%. Assume the population of grades on history exams is known to be distributed Normally, with a standard deviation of 14%. Approximately what percent of students earn a score between 75% and 89%?

A. 14%

B. 34.1%

C. 15.7%

D. 38.5%

E. 50%

When a certain coin is flipped, the probability of obtaining a tails is 0.60. Which of the following is the probability that tails would be obtained exactly 10 times when the coin is flipped 20 times?

A. 0.0473

B. 0.1171

C. 0.1762

D. 0.2447

E. 0.50

Answer 1

#1.
z = (x - μ)/σ
z1 = (75 - 89)/14 = -1
z2 = (89 - 89)/14 = 0

Therefore, we get
P(75 <= X <= 89) = P((89 - 89)/14) <= z <= (89 - 89)/14)
= P(-1 <= z <= 0) = P(z <= 0) - P(z <= -1)
= 0.5 - 0.1587
= 0.341

Option B

#2.
Here, n = 20, p = 0.6, (1 - p) = 0.4 and x = 10
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X = 10)
P(X = 10) = 20C10 * 0.6^10 * 0.4^10
P(X = 10) = 0.1171

Option B