Question

The life of a Radio Shack record player is normally distributed with a mean of 3 years and a standard deviation of 1 years. Radio Shack guarantees its record players for 2 years.

Answer 1

The life of a Radio Shack record player is normally distributed with a mean of 3 years and a standard deviation of 1 years. Radio Shack guarantees its record players for 2 years.

Find the probability that a record player will last less than 2 years?

Answer:

the  probability that a record player will last less than 2 years is 0.1586

Step-by-step explanation:

Given that:

A mean which is normally distributed = 3

and a standard deviation = 1

The objective is to find that a record player will last less than 2 years

Let X be the random variable

i.e

$P(X<2) = P( \dfrac{X - \mu}{\sigma}<\dfrac{X - \mu}{\sigma})$

$P(X<2) = P( \dfrac{2 - \mu}{\sigma}<\dfrac{2 - 3}{1})$

$P(X<2) = P( Z< \dfrac{-1}{1})$

$P(X<2) = P( Z< -1)$

From the standard normal tables :

$P(X<2) = 1- P( Z< 1)$

$P(X<2) = 1- 0.8414$

P(X < 2) = 0.1586

Therefore; the  probability that a record player will last less than 2 years is 0.1586