Question

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 3.7 years, and standard deviation of 1 years. The 7% of items with the shortest lifespan will last less than how many years? Give your answer to one decimal place.

Answer 1

Answer:

2.2 years

Step-by-step explanation:

Mean lifespan (μ) = 162 degrees

Standard deviation (σ) = 1 year

The 7th percentile of a normal distribution has an equivalent z-score of roughly z = -1.475. The lifespan, X, at the 7th percentile is given by:

$z=\frac{X-\mu}{\sigma} \\-1.475=\frac{X-3.7}{1}\\ X=2.2\ years$

The 7% of items with the shortest lifespan will last less than 2.2 years.