The manager of a local gym has determined that the length of time members spend at the gym is a normally distributed variable with a mean of 80 minutes and a standard deviation of 20 minutes.

Question

What proportion of members spend less than 55 minutes at the gym? Use the standard normal distribution tables of your Wegner textbook. Give your answer to the nearest percentage, e.g. 54% or 28% (remember to include the % sign!!!).

(Based on Wegner, Exercise 19, p149, 3rd ed / Exercise 8.17, p208, 2nd ed)

Answer 1

The manager of a local gym has determined that the length of time members spend at the gym is a normally distributed variable with a mean of 80 minutes and a standard deviation of 20 minutes.

What proportion of members spend less than 55 minutes at the gym?

Answer 2

Z = (score-mean)/SD

Find table in the back of your statistics text (Wegner?) labeled something like "areas under normal distribution" to find the proportion/probability related to the Z score. Multiply by 100.

Answer 3

75