A recent study of the lifetimes of cell phones found the average is 24.3 months. the standard deviation is 2.6 months. if a company provides its 33 employees with a cell phone, find the probability that the mean lifetime of these phones will be less than 23.8. assume cell phone life is normally distributed variable.

Question

Charity Wu

Mathematics

8 August, 02:45

A recent study of the lifetimes of cell phones found the average is 24.3 months. the standard deviation is 2.6 months. if a company provides its 33 employees with a cell phone, find the probability that the mean lifetime of these phones will be less than 23.8. assume cell phone life is normally distributed variable.

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Marco Banks · Answer 1

To answer this problem, we assume that the data is normally distributed so that we can use the z score. the formula for z score is

z = - (mean-data) / standard deviation

Substituting,

z = - (24.3-23.8) / 2.6 = - 0.1923

checking out from the z-table, probability is equal to 0.4247 or 42.47 percent.