Question

Mr. Mario Mendoza is a famous baseball player (Shortstop) in the Major League Baseball. Usually, he can successfully hit 2 out of 10 at bats. Therefore, the Mendoza line is named after him.

1. In a particular season, he attempted 100 at bats. Define X as the number of hits he will have. Write down how X is distributed.
2. What is the probability that he makes exactly 25 hits? (There are two ways to do this part, either way is fine.)  
3. Construct a 90% Confidence Interval for the average number of hits he will have in 100 at bats

Answer 1

a)

P(hit) =2/10 =0.2

this is be a binomial distribution with n = 100 and p =0.2

b)

This is a binomial distribution question with

n = 100

p = 0.2

q = 1 - p = 0.8where

c) Since we know that

Confidence interval(in %) = 90

z @ 90.0% = 1.645

Since we know that

Required confidence interval = (20.0-0.658, 20.0+0.658)

Required confidence interval = (19.342, 20.658)