Question

Consider the probability that at most 93 out of 127 students will pass their college placement exams. Assume the probability that a given student will pass their college placement exam is 53%. Specify whether the normal curve can be used as an approximation to the binomial probability by verifying the necessary conditions.
the answer will be in yes or no format

Answer 1

Answer:

Yes, the normal curve can be used as an approximation to the binomial probability.

Step-by-step explanation:

Let X = number of students that pass their college placement exam.

The probability that a given student will pass their college placement exam is, P (X) = p = 0.53.

A random sample of n = 127 students is selected.

The random variable X follows a Binomial distribution.

But the sample size is too large.

A Normal approximation to Binomial can be used to approximate the distribution of proportion p.

The conditions to be satisfied are:

• np ≥ 10
• n(1-p) ≥ 10

Check whether the conditions are satisfied as follows:

$np=127\times0.53=67.31>10$

$n(1-p)=127\times(1-0.53)=59.69>10$

Both he conditions are satisfied.

Thus, a normal curve can be used as an approximation to the binomial probability.