Normal Curve Applications

Question

The amounts of time per workout an athlete uses a stairclimber are normally​ distributed, with a mean of 24 minutes and a standard deviation of 7 minutes. Find the probability that a randomly selected athlete uses a stairclimber for​ (a) less than 19 ​minutes, (b) between 24 and 31 ​minutes, and​ (c) more than 40 minutes.

Answer 1

19-24 = -5

-5/7 = about -.7143 = z score

use a z calculator

Pr(<19) = 0.2375 = 23.75%

31-24 = 7

7/7 = 1 = z score

uese the empirical rule

68% lie within 1 standard deviation

half that is 34% between 0 and 1 standard devation

34% is the probability of 24 to 31 minutes

or use a z calculator or z table for more accurate solution

34.134%

more than 40 minutes?

40-24 = 16

16/7 = about 2.2857 = z score

use a z table or calculator

0.011136 = 1.1136%

using the empirical rule 95-99.7

to the right of 2 standard deviation is 2.5%

to the right of 3 standard deviations is 0.3%

to the right of 1.1136 standard deviations is between 2.5 and 0.3

.3<1.1136< 2.5