Question

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 34 employees with a cell phone, find the probability that the mean lifetime of these phones will be less than 23.8 months. Assume cell phone life is a normally distributed variable.
P(x < 23.8) =

Answer 1

Solution :

Let X be a random variable which represents the lifetime of cell phones.

Given that,

Mean (μ) = 24.3 months

Standard deviation (σ) = 2.6 months

Sample size (n) = 34

We have to obtain P(x̄ < 23.8).

(Where, x̄ is mean lifetime of 34 cellphones).

We know that if X ~ N(μ, σ²) then  x̄ ~ N(μ, σ²/n)

And if x̄ ~ N(μ, σ²/n) then,

Using "pnorm" function of R we get, P(Z < -1.1213) = 0.1311

Hence, the probability that the mean lifetime of 34 phones will be less than 23.8 months is 0.1311.

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