216k views
1 vote
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.

User Kazutaka
by
7.7k points

1 Answer

4 votes

Answer:

2.2 years

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=(X-\mu)/(\sigma) \\-1.475=(X-3.7)/(1)\\ X=2.2\ years

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

User Overachiever
by
8.8k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories