HW #5 T, 11/19
Problem 1
Suppose you have a random variable X that represents the lifetime of a certain brand of
light bulbs. Assume that the lifetime of light bulbs are approximately normally
distributed with mean 1400 and standard deviation 200 (in other words X ~ N(1400,
200
2
)).
Answer the following using the standard normal distribution table:
a) Approximate the probability of a light bulb lasting less than 1250 hours.
b) Approximate the probability that a light bulb lasts between 1360 to 1460 hours.
c) Approximate the probability that a light bulb lasts more than 1500 hours.
d) Draw this distribution’s shape. Note the value of X that is in the middle of the
distribution and use the empirical rule to approximate the values that contain the middle
68% and 95% of all observations.
Problem 2
Suppose you now take samples of size 16 from this population of light bulbs.
a)
How are these sample means distributed? Be as specific as you can about the type
of distribution and give values for the mean and standard error.
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 Spring '08
 Stefeni
 Empirical Rule, Normal Distribution, Standard Deviation

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