11. Suppose a company claims that their lightbulb lasts an average of 5 years with astandard deviation of 0.5 years. (They are claiming that the population mean life of thebulb is 5 years with a population standard deviation of 0.5 years.) Assume theselightbulb lifetimes are normally distributed.a. Suppose you buy one light bulb and it only lasts you 4.5 years. Would you consider thatevidence against the company’s claim? (Hint: Assuming that the company’s claim istrue, determine the probability that a randomly selected bulb would last 4.5 years orless.)b. Suppose you buy 10 bulbs, and these 10 bulbs have a mean life of 4.5 years. Would youconsider that evidence against the company’s claim? (Hint: Assuming the company’sclaim is true, determine the probability that the mean of 10 randomly selected bulbswould last 4.5 years or less.)
11. Suppose a company claims that their lightbulb lasts an average of 5 years with a
standard deviation of 0.5 years. (They are claiming that the population mean life of the
bulb is 5 years with a population standard deviation of 0.5 years.) Assume these
lightbulb lifetimes are normally distributed.
a. Suppose you buy one light bulb and it only lasts you 4.5 years. Would you consider that
evidence against the company’s claim? (Hint: Assuming that the company’s claim is
true, determine the probability that a randomly selected bulb would last 4.5 years or
less.)
b. Suppose you buy 10 bulbs, and these 10 bulbs have a mean life of 4.5 years. Would you
consider that evidence against the company’s claim? (Hint: Assuming the company’s
claim is true, determine the probability that the mean of 10 randomly selected bulbs
would last 4.5 years or less.)
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