The time per workout an athlete uses a stair climber is norm

The time per workout an athlete uses a stair climber is normally distributed, with a mean of 22 minutes and a standard deviation of 6 minutes. An athlete is randomly selected.

Find the probability that the athlete uses a stair climber between 23 and 29 minutes.

Solution

First, recall that a normal distribution extends approximately three standard deviations above and below the mean. Thus, the time on the stair climber will probably be within 6 standard deviations, or 3*6 = 18 minutes. Thus, the possible values of time will extend from 22 - 18 = 4 to 22 + 18 = 40.

Will create a column of Minutes ranging from 6 to 40, in one minute increments.

Use EXCEL to create NORMDIST function.

EXCEL PROCEDURE:

Use the NORMDIST function to generate a column of Area to the Left. This function has the format NORMDIST(x,mean,stddev,true).   In this case, the formula for cell K12 will look like: =NORMDIST(J12,22,6,true) .

The EXCEL result is pbtained as follows,

To Find the probability that the athlete uses a stair climber between 23 and 29 minutes.

The answer is the area between 23 and 29. Since the table gives Area to the Left, look up 29 and 23, then subtract the area. That is, P(23<x<29) = 0.878327 - 0.566184 = 0.312143 = 31.21%  

The probability that the athlete uses a stair climber between 23 and 29 minutes is 31.21%.