1. An automobile battery manufacturer claims that its midgrade battery has a mean life of 50 months with a standard deviation of 6 months. Suppose the distribution of battery lives of this particular brand is approximately normal. On the assumption all of this is true: (a) Let X = number of months a battery will last. Find the probability that a single battery of this type will last longer than 51 months. (4 decimals) (b) Find the probability that the mean of a random sample of 36 batteries will be over 51 months. (c) Why do you think the values from part (b) and part (c) are different? Explain.
1. An automobile battery manufacturer claims that its midgrade battery has a mean life of 50 months with a standard deviation of 6 months. Suppose the distribution of battery lives of this particular brand is approximately normal. On the assumption all of this is true: (a) Let X = number of months a battery will last. Find the probability that a single battery of this type will last longer than 51 months. (4 decimals) (b) Find the probability that the mean of a random sample of 36 batteries will be over 51 months. (c) Why do you think the values from part (b) and part (c) are different? Explain.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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Transcribed Image Text:1. An automobile battery manufacturer claims that its midgrade battery has a
mean life of 50 months with a standard deviation of 6 months. Suppose the
distribution of battery lives of this particular brand is approximately normal. On
the assumption all of this is true:
(a) Let X = number of months a battery will last. Find the probability that a single
battery of this type will last longer than 51 months. (4 decimals)
(b) Find the probability that the mean of a random sample of 36 batteries will be
over 51 months.
(c) Why do you think the values from part (b) and part (c) are different? Explain.
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