The average lifetime of a light bulb is 3000 hours with a standard deviation of 696 hours. A simple random sample of 36 bulbs is taken. (a)  What are the expected value, standard deviation, and sampling distribution of x? (b)  What is the probability that the average life time in the sample will be between 2670.56 and 2809.76 hours? (c)  What is the probability that the average life time in the sample will be equal to or greater than 3219.24 hours? (d)  What is the probability that the average life time in the sample will be equal to or less than

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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The average lifetime of a light bulb is 3000 hours with a standard deviation of 696 hours. A
simple random sample of 36 bulbs is taken.
(a)  What are the expected value, standard deviation, and sampling distribution of
x?
(b)  What is the probability that the average life time in the sample will be between 2670.56 and
2809.76 hours?
(c)  What is the probability that the average life time in the sample will be equal to or greater
than 3219.24 hours?
(d)  What is the probability that the average life time in the sample will be equal to or less than
3180.96 hours? 

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