A manufacturer knows that their items have a normally distributed lifespan, with a mean of 9.9 years, and standard deviation of 3 years. The 9% of items with the shortest lifespan will last less than how many years? Give your answer to one decimal place. Submit Question

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 9.9 years, and standard deviation of 3 years. The 9% of items with the shortest lifespan will last less than how many years? Give your answer to one decimal place. Submit Question

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.3: Measures Of Spread

Problem 26PFA

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Expert Solution

Step 1

Normal distribution is used for calculating the probability of a continuous variable when the data is more or less symmetric. So, a normal distribution curve is bell shaped, in which the highest point of the curve indicates the value of the highest probability, and the values of probability decrease on both sides of the curve and eventually become zero.

The formula to compute the z-score is:

$z - s c o r e = \frac{R a w s c o r e - P o p u l a t i o n m e a n}{S \tan d a r d d e v i a t i o n}$