Question

We collected data on the tuition charged by colleges and universities in Michigan. Here are some numerical summaries for the data

Mean 10,614
SD 8049
Min 1873
Max 30,823

Based on the relationship between the mean, standard deviation, minimum, and maximum, is it reasonable to believe that the distribution of Michigan tuitions is approximately Normal?

A)It could be if the median is close to the mean.

B)No, because the minimum is too close to the mean.

C)No, because the maximum is too close to the mean.

D)(INCORRECT)We do not have enough information to say whether the distribution is approximately Normal.

E)No, because the standard deviation is too high

Answer 1

A high standard deviation relative to the mean and a wide range between the minimum and maximum tuition fees suggest the distribution of Michigan tuitions is likely not normal, supporting answer choice E.

Step-by-step explanation:

When evaluating whether the distribution of tuition fees for colleges and universities in Michigan is approximately normal, the summary statistics provided include a mean of $10,614, a standard deviation (SD) of $8,049, a minimum fee of $1,873, and a maximum fee of $30,823.

The large standard deviation relative to the mean suggests significant variability in tuition fees, and the minimum and maximum values show a wide range in the data. This makes it less likely for the distribution to be normal.

Option E, which states 'No, because the standard deviation is too high' is the most reasonable answer given these statistics. A high standard deviation in relation to the mean suggests that the data values are spread out over a wide range, which is not characteristic of a normal distribution where most values are clustered around the mean.

Moreover, the fact that there is a very low minimum tuition and a very high maximum tuition fee further indicates that the distribution could be skewed, which departs from the symmetry of a normal distribution.