Question

The distribution of room and board expenses per year at a four-year college is normally distribute with a mean of $5850 and standard deviation of $1125. Random samples of size 20 are drawn from this population and the mean of each sample is determined. Which of the following mean expenses would be considered unusual?a) 5180b)6180c)6350

Answer 1

a) 5180

Explanation:

We must calculate with respect to each of the options:

a) 5180

We have that the mean (m) is equal to 5850, the standard deviation (sd) 1125 and the sample size (n) = 20

They ask us for P (x <5180)

For this, the first thing is to calculate z, which is given by the following equation:

z = (x - m) / (sd / (n ^ 1/2))

We have all these values, replacing we have:

z = (5180 - 5850) / (1125 / (20 ^ 1/2))

z = -2.66

With the normal distribution table (attached), we have that at that value, the probability is:

P (z <-2.66) = 0.0039

Which means that the probability is 0.39%, which is a very low probability, which is not necessary to calculate the other options, we already know that this data is very unusual.