“Quiz 11” Central Limit Theorem & Confidence Intervals
May 5, 2004
1. (From p. 349 #6). The heights of 18 year-old men are approximately normally
distributed, with mean 68 inches and standard deviation 3 inches.
(a) What is the probability that an 18 year-old man selected at random is between 67 and
69 inches tall.
(b) If a random sample of nine 18 year-old men is selected, what is the probability that
the mean height of the sample is between 67 and 69 inches?
(c) Why was the probability in (b) higher than that in (a)?
(d) Would you expect the probability that an 18 year-old man selected at random is more
than 74 inches tall to be lower, the same as, or higher than the probability of selecting a
random sample of nine eighteen year-old men with a mean height of more than 74
inches?
2. (From p. 349 # 18). The taxi and takeoff time for commercial jets is a random variable
x with mean 8.5 minutes and standard deviation of 2.5 minutes. You may assume the jets
are lined up on the runway so that one taxis and takes off immediately after the other, and
they take off one at time on a given runway. What is the probability that for 36 jets on a
given runway total taxi and take off time will be
(a) less than 320 minutes?
(b) more than 275 minutes?
(c) between 275 and 320 minutes?
3. (From p. 385 #6) The Roman Arches is an Italian restaurant. The manager wants to
estimate the average amount a customer spends on lunch Monday through Friday. A
random sample of 115 customers' lunch tabs gave a sample mean of $9.74 with a sample
standard deviation s = $2.93.
(a) Find a 95% confidence interval for the average amount spent on lunch by all
customers.
(b) For a day when the Roman Arches has 115 lunch customers, use part (a) to estimate
the range of dollar values for the total lunch income that day.