Respuesta :
Answer:
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:
[tex]z=\frac{X-\mu}{\sigma}[/tex]
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:
[tex]P(X<5)=P(\frac{X-\mu}{\sigma}<\frac{5-10.5}{3})\\[/tex]
[tex]=P(Z<-1.83)\\=1-P(Z<1.83)\\=1-0.9664\\=0.0336\\\approx 3.4\%[/tex]
Thus, the fraction of washer that will need repair or replacement within the guarantee period is 3.4%.
