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.
<h3>What is a normal distribution?</h3>
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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