Question

1) A baseball player has a batting average of 0.332. would it be unusual if he hits 22 of his next 90 at-bats?

2)The scores on a midterm exam are normally distributed and have a mean score of 78 and a standard deviation of 7. The top 15% of all scores are designated as A's. You earn an 89 on the midterm exam. Is your considered an A?

Answer 1

(1) it is a binomial distribution with p = 0.332 and n = 90

we have to find the probability of P(X=22)

using the formula

this probability is less than 0.05, so it is unusual to hit 22 at bats out of 90

(2) Given mean = 78 and standard deviation sd = 7

z score corresponding to top15% or bottom 85% is 1.036 (using z percentile table)

Minimum score for A = mean +(z*standard deviation)

= 78+(1.036*7)

= 85.25

Therefore, 89 is above minimum score required to get an A. So, 89 must be considered as an A