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%.

answer: expected value of x = 1.0

step-by-step explanation:

p(x=0) = 0.25

p(x=1) = 0.50

p(x=2) = 0.25

expected value for x = 0×0.25 + 1×0.5 + 2×0.25 = 1.0