Question

The toasters produced by a company have a normally distributed life span with a mean of 5.8 years and a standard deviation of 0.9 years, the company is willing to have a warranty that replaces at most 5% of their toasters sold. What is the longest a blender can last and still be in the lowest 5% of life spans?
4.6 years

7.3 years

4.3 years

5.9 years

Answer 1

The longest a blender can last and still be in the lowest 5% of life spans will be 4.6 years. The correct option is A.

What is a normal distribution?

The z-score formula can be used to resolve issues with samples that have a normal distribution. The score of a measure X in a collection with mean and standard deviation is given by:

Z = ( X - μ ) / σ

The Z-score calculates the deviation of the measure from the mean in standard deviations. We glance at the z-score table after determining the Z-score to determine the p-value connected to it.

The likelihood that the measure's value is less than X, or the percentile of X, is represented by this p-value. The likelihood that the value of the measure is greater than X is obtained by deducting 1 from the value.

In this problem, we have that:

μ = 5.8, σ = 0.9

Only those on the 5th percentile or lower will be replaced. So the warranty is the value of X when Z has a value of 0.05.

The value of x will be:-

Z = ( X - μ ) / σ

-1.28 = ( X - 5.8 ) / 0.9

X = 4.6

Therefore, the longest a blender can last and still be in the lowest 5% of life spans will be 4.6 years. The correct option is A.

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