The average lifetime of a light bulb is 3,000 hours with a standard deviation of

Question

The average lifetime of a light bulb is 3,000 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 shape of the sampling distribution of xbar?

b. What is the probability that the average life in the sample will be between 2,675.56 and 2,809.76 hours?

c. What is the probability that the average life in the sample will be greater than 3,219.24 hours?

d. What is the probability that the average life in the sample will be less than 3,180.96 hours?

Explanation / Answer

a. The expected value of a sample average is the same as the population mean, 3000. The standard deviation in the average is the population standard deviation divided by n, so 696/36 = 116. The distribution is approximately normal.

b. P[2675.56 < average < 2809.76] = P[(2675.56 - 3000)/116 < z < (2809.76 - 3000)/116] = 0.0479.

c. P[3219.24 < average] = P[(3219.24 - 3000)/116 < z] = 0.0294

d. P[average < 3180.96] = P[z < (3180.96 - 3000)/116] = 0.9406.

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