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On the average, members at a local fitness center work out for 90 minutes with a...

On the average, members at a local fitness center work out for 90 minutes with a standard deviation of 15 minutes. The distribution is normal.

9. What percentage of the fitness club members work out for 45 minutes or less? What percent does that leave in each tail?

10. What percentage of fitness club members work out for 2 hours and 15 minutes or more? What percent does that leave in each tail?

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Answer #1

If it is a normal distribution, then the distribution of the random variable function in the following pattern.

68% of the area is within one SD of the mean  

95% of the area is within two SDs of the mean

99.7% of the area is within three SDs of the mean.

a) In the problem it is given that the the percentage of the population working for less than or equal to 45 minutes.

The answer is, (100-99.7)/2 0.13%

The percentage in each tail is 0.13%

b) percentage of fitness club members work out for 2 hours and 15 minutes or more is 2.1%.

  The percentage in each tail is 2.1%

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