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

To find the probability that a CD player will break down during the guarantee period, calculate the area under the normal curve from x = 0 to x = 3.

Step-by-step explanation:

To find the probability that a CD player will break down during the guarantee period, we need to calculate the area under the normal curve from x = 0 to x = 3. Using the given mean, standard deviation, and guarantee period, we can calculate the z-scores for both values and then find the area using a standard normal distribution table or a calculator.

First, we calculate the z-score for x = 0:

z = (0 - 4.1) / 1.3 = -3.15

Next, we calculate the z-score for x = 3:

z = (3 - 4.1) / 1.3 = -0.85

Using these z-scores, we can find the corresponding probabilities using a standard normal distribution table or a calculator. The area under the curve from z = -3.15 to z = -0.85 represents the probability that a CD player will break down during the guarantee period.

Answer 2

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( (X - \mu)/(\sigma)<(X - \mu)/(\sigma))`

`P(X<2) = P( (2 - \mu)/(\sigma)<(2 - 3)/(1))`

`P(X<2) = P( Z< (-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