Part A:
For problems 1 - 4, draw the necessary pictures so that I may follow your work. Label all
z-scores and areas. Assume that we have a normal distribution with a.
(5 pts each)
1. P(x < 75) = __________ 2. P(73 < x < 93) = __________
3. P(x <73 or x > 75) = __________ 4. P(x = 73) = ___________
Part B: Determine whether each statement is true or false.
If the statement is false, explain why.
(15 points = 3pts each)
1. The total area under the normal distribution bell-shaped curve is infinite.
2. The standard normal distribution is a discrete distribution.
3. The z value corresponding to a number below the mean is always negative.
4. The area under the standard normal distribution to the left of z = 0 is negative.
5. For a standard normal probability distribution, the mean is always 1.
Part C:
Work the following problems. Please show your work to receive full credit.
1. (15pts) 30 High school students were randomly selected and surveyed about the amounts of time they spend at after-school jobs. The mean and standard deviation were found to be 26 hours and 6 hours, respectively. Assume that the given statistics come from a normally distributed population.
a. Find the best point estimate of the population standard deviation.
b. Find a 95% confidence interval for the population standard deviation.
2. (10pts) You have just been hired by General Motors to tour the United States giving randomly selected drivers test rides in a new Corvette (yeah, right!). After giving the test drive, you must ask the rider whether he or she would consider buying a Corvette. How many riders must you survey (take for test rides) to be 90% confident that the sample proportion is off by no more than five percentage points?
3. (10pts) Of 2590 students randomly selected, 98% of them own computers. Construct a 99% confidence interval for the true proportion of all students who own computers.
4. (15pts) A food packing company fills sacks of cereal using automated machinery. The fill amounts are normally distributed with a mean weight of 2 pounds and a standard deviation of 0.20 pounds.
a) One sack is randomly selected. What is the probability that the weight of the sack exceeds 2.05 pounds?
b) Sixteen sacks are randomly selected. What is the probability that the mean weight of the sample of 16 sacks exceeds 2.05 pounds?
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