A) The average lifetime of a battery is normally distributed with mean of 50 hou

Question

A) The average lifetime of a battery is normally distributed with mean of 50 hours and STD of 5 hours. Find the approximate 40th percentile of battery lifetimes.

B) You are told a population of batteries has a mean battery life = 175 hours and standard deviation = 20 hours What is the probability that a randomly selected battery from this population has a battery life of either > 240 hr. OR < 174.7 hr.?

Please show all work clearly. Please do work by hand and do not use excel. Thank you very much for your help

Explanation / Answer

A) Mean = 50 hours

Standard deviation = 5 hours

P(X < A) = P(Z < (A - mean)/standard deviation)

Here, its given that P(X < A) = 0.4

So, P(Z < (A - 50)/5) = 0.4

From standard normal distribution table,

(A - 50)/5 = -0.25

A = 48.75 hours

Approximate 40th percentile of battery lifetimes = 48.75 hours

B)   = 175 hours

= 20 hours

P(X > 240) or P(X < 174.4) = 1 - P(X< 240) + P(X < 174.7)

= 1 - P(Z < (240-175)/20) + P(Z < (174.7-175)/20

= 1 - P(Z < 3.25) + P(-0.015)

= 1 - 0.9994 + 0.4940

= 0.4946

Probability that a randomly selected battery from this population has a battery life of either > 240 hr. OR < 174.7 hr = 0.4946

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