Which of the following terms is best described as the point halfway between
the endpoints of a line segment?
o
a. coordinate
o
b. vertex
o
c. midpoint
o
d. ordered pair

Using the normal distribution and the central limit theorem, it is found that:

a) Since both and , a normal approximation can be used.b) There is a 0.0475 = 4.75% probability that the proportion in the random sample of 100 orders is the same as the proportion found in the audit sample or less.Normal Probability Distribution

In a normal distribution with mean and standard deviation , the z-score of a measure X is given by:

It measures how many standard deviations the measure is from the mean.  After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.By the Central Limit Theorem, for a proportion p in a sample of size n, the mean is and the standard error is , as long as both and .

In this problem:

90% of customer orders are received within three working days, hence Sample of 100 orders, hence .

The mean and the standard error are given by:

Item a:

Since both and , a normal approximation can be used.

Item b:

The probability is the p-value of Z when , hence:

By the Central Limit Theorem

has a p-value of 0.0475.

There is a 0.0475 = 4.75% probability that the proportion in the random sample of 100 orders is the same as the proportion found in the audit sample or less.

To learn more about the normal distribution and the central limit theorem, you can take a look at link