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

a) 5180

Step-by-step 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.