Answered: rs. a. What is the probability that the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

A computer battery has a normal distribution with an average life span of 10 hours and a standard deviation of 3 hours.
a. What is the probability that the computer battery will last between 10 and 14 hours?
b. Find out how many hours at least 12% of the computer batteries with the longest endurance.
c. A company bought 10 of these computers. What is the probability that the battery life of at least 2 of the purchased computers is within the range specified in “a”?

Expert Solution

Part a

$\begin{array}{rcl} P (10 & < & X < 14) = P (\frac{10 - 10}{3} < z < \frac{14 - 10}{3}) \\ = & P (0 < z < 1.33) \\ = & P (z < 1.33) - P (z < 0) \\ = & 0.9082 - 0.5000 \\ = & 0.4082 \end{array}$

Therefore the probability that the computer battery will last between 10 and 14 hours is 0.4082

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