Question

Consider the probability that more than 66 out of 125 students will not pass their college placement test. Assume the probability that a given student will not pass their college placement test is 1%. Specify whether the normal curve can be used as an approximation to the binomial probability by verifying the necessary conditions. Yes or No?

Answer 1

Here,

n = 125 (sample size)

Let p be the probability that a given student will not pass their college placement test

p = 1%/100% = 0.01 (population proportion)

q = (1 - p) = (1 - 0.01) = 0.99

The normal curve can be used as an approximation to the binomial probability if (n p) and (n q) both are greater than 5

n p = 125 0.01 = 1.25

n q = 125 0.99 = 123.75

Here (n p) is less than 5 so, normal curve can not be used as an approximation to the binomial probability.

Answer: No