Washers The life span of a type of automatic washer is approximately normally distributed with mean and standard deviation equal to and years, respectively. If this type of washer is guaranteed for a period of years, what fraction will need to be repaired and/or replaced?

The fraction of washer that will need repair or replacement within the guarantee period is 3.4%.

Step-by-step explanation:

Let X = lifespan of automatic washer (in years).

The lifespan of automatic washer is normally distributed with mean lifespan, μ = 10.5 years and standard deviation σ = 3 years.

To compute the probability of a normal distribution it is better to standardize the raw scores (X).

The raw score can be standardized using the formula:

These standardized scores are known as z-scores.

The distribution of z-scores follows a normal distribution with mean 0 and variance 1. The distribution is also known as Standard Normal distribution.

Now, it is provided that this type of washer has a guarantee period of 5 years, i.e. within 5 years it would either need repair or replacement.

Compute the probability that the washer will need repair or replacement within 5 years as follows:

Thus, the fraction of washer that will need repair or replacement within the guarantee period is 3.4%.

15 units use socratic

step-by-step explanation: 15 units

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x