Question

Consider the probability that fewer than 46 out of 134 students will not pass their college placement exams. Assume the probability that a given student will not pass their college placement exam is 98%. Specify whether the normal curve can be used as an approximation to the binomial probability by verifying the necessary conditions.

a. Yes
b. No

Answer 1

b. No

Explanation:

Binomial approximation to the normal:

Binomial distribution has n trials, with p probability.

If

`np \geq 10` and
`n(1-p) \geq 10`, it can be approximated to the normal distribution.

Assume the probability that a given student will not pass their college placement exam is 98%.

This means that
`p = 0.98`

134 students:

This means that
`n = 134`

Necessary conditions:

`np = 134*0.98 = 131.32 \geq 10`

`n(1-p) = 134*0.02 = 2.68 < 10`

Since the necessary condition n(1-p) < 10 is not satisfied, the answer is No, given by option b.