Question

wants to know if it's incoming frosh feel prepared to succeed at college. They sample 100 students and ask them this question, and receive an answer of 67% saying "yes, I feel prepared". They repeat this many times. This is a situation where the Central Limit Theorem is applicable to calculate probabilities. Use the CLT to estimate the probability that more than 70% of all students would say they "feel prepared".

Please the answer with explanation.

Thank you!

Answer 1

Answer)

N = 100

P = 0.67

First we need to check the conditions of normality that is if n*p and n*(1-p) both are greater than 5 or not

N*p = 67

N*(1-p) = 33

Both the conditions are met so we can use standard normal z table to estimate the probability

z = (oberved p - claimed p)/standard error

Standard error = √{claimed p*(1-claimed p)/√n

Observed p = 0.7

Claimed = 0.67

N = 100

Z = 0.64

From z table, P(z>0.64) = 0.2611