Question

The number of incoming students at two campuses of a midwestern university have historically been normally distributed. The main campus incoming class has a mean of 3,507 and a standard deviation of 375, and the regional campus incoming class has a mean of 740 and a standard deviation of 114. If there were 3,838 incoming students on the main campus and 848 on the regional campus, which had the more successful year in student recruitment based on z scores

Answer 1

Due to the higher z-score, the regional campus had the more successful year in student recruitment.

Explanation:

Z-score:

In a set with mean
`\mu` and standard deviation
`\sigma`, the z-score of a measure X is given by:

`Z = (X - \mu)/(\sigma)`

The Z-score 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. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The main campus incoming class has a mean of 3,507 and a standard deviation of 375. There were 3,838 incoming students on the main campus.

We have to find Z, considering
`X = 3838, \mu = 3507, \sigma = 375`

So

`Z = (X - \mu)/(\sigma)`

`Z = (3838 - 3508)/(375)`

`Z = 0.88`

Regional campus incoming class has a mean of 740 and a standard deviation of 114. 848 students on the regional campus.

We have to find Z when
`X = 848, \mu = 740, \sigma = 114`.

So

`Z = (X - \mu)/(\sigma)`

`Z = (848 - 740)/(114)`

`Z = 0.95`

Which had the more successful year in student recruitment based on z scores?

Due to the higher z-score, the regional campus had the more successful year in student recruitment.