Probability & Statistics

Start Free Trial

The amount of time per workout an athlete uses a stair climber are normally distributed, with a mean of 20 minutes and a standard deviation of 7 minutes. Find the probability that a randomly selected athlete uses a stair climber for (a) less than 16 minutes, (b) between 20 and 28 minutes, and (c) more than 30 minutes

For part A, the probability is 28.3%. For part B, it is 37.4%. For part C, it is 7.6%. You can find these answers using a normal distribution calculator.

Expert Answers

An illustration of the letter 'A' in a speech bubbles

Remember that when discussing standard deviation and the mean, 68% of values in a data set will fall within one standard deviation of the mean, 95% will fall within 2 standard deviations of the mean, and 99.7% will fall within 3 standard deviations. This goes in both directions (above and below the mean), so in this scenario, 68% of athletes will use the stair climber between 13 and 27 minutes, 95% between 6 and 34 minutes, and 99.7% between 0 and 41 minutes.

However, none of these values are listed in the problem. To solve the problem, we need to use a z-table or normal distribution calculator. I used a normal distribution calculator. The calculator will ask you to specify the mean and standard deviation as well as the probability you are trying to find. In part a of the problem, we want to find the probability that an athlete uses the stair stepper for less than 16 minutes, so we will put 16 in the "below" box and hit "recalculate." The probability is .283, or 28.3%. Part B of the problem asks us to find the probability of an athlete using the stair stepper between 20 and 28 minutes, so we will put those values in the "between" boxes. That value is 37.4%. Finally, for Part C, we will put 30 in the "above" box. The probability here is 7.6%.

I have linked the normal distribution calculator I used to help you with future problems.

Approved by eNotes Editorial Team