# Question

Did you ever buy an incandescent light bulb that failed (either burned out or did not work) the first time you turned the light switch on? When you put a new bulb into a light fixture, you expect it to light, and most of the time it does. Consider 8-packs of 60-watt bulbs and let x be the number of bulbs in a pack that “fail” the first time they are used. If 0.02 of all bulbs of this type fail on their first use and each 8-pack is considered a random sample,

a. List the probability distribution and draw the histogram of x.

b. What is the probability that any one 8-pack has no bulbs that fail on first use?

c. What is the probability that any one 8-pack has no more than one bulb that fails on first use?

d. Find the mean and standard deviation of x.

e. What proportion of the distribution is between m _ σ and m + σ

f. What proportion of the distribution is between m _ 2σ and m + 2σ

g. How does this information relate to the empirical rule and Chebyshev’s theorem? Explain.

h. Use a computer to simulate testing 100 8-packs of bulbs and observing x, the number of failures per 8-pack. Describe how the information from the simulation compares with what was expected (answers to parts a–g describe the expected results).

i. Repeat part h several times. Describe how these results compare with those of parts a–g and with part h.

a. List the probability distribution and draw the histogram of x.

b. What is the probability that any one 8-pack has no bulbs that fail on first use?

c. What is the probability that any one 8-pack has no more than one bulb that fails on first use?

d. Find the mean and standard deviation of x.

e. What proportion of the distribution is between m _ σ and m + σ

f. What proportion of the distribution is between m _ 2σ and m + 2σ

g. How does this information relate to the empirical rule and Chebyshev’s theorem? Explain.

h. Use a computer to simulate testing 100 8-packs of bulbs and observing x, the number of failures per 8-pack. Describe how the information from the simulation compares with what was expected (answers to parts a–g describe the expected results).

i. Repeat part h several times. Describe how these results compare with those of parts a–g and with part h.

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