Review from before Christmas Break
Directions: Show all work!
1.
The duration of human pregnancies can be described by a normal distribution with a mean of 266 days
and a standard deviation of 16 days.
a. What percentage of pregnancies should last between 270 and 280 days?
b. At least how many days should the longest 25% of all pregnancies last?
c.
Suppose a certain obstetrician is currently providing prenatal care to 60 pregnant women.
What’s the probability that the mean duration for his 60 patients will be less than 260 days?
2. State police believe that 70% of the drivers traveling on a major interstate highway exceed the speed
limit.
a. What’s the probability that a randomly selected driver is exceeding the speed limit?
b. The police plan to set up a radar trap and check the speeds of 80 cars. What’s the probability
that more than 75% of them are exceeding the speed limit?
3. Grocery store receipts show that customer purchases have a skewed distribution with a mean of $32
and a standard deviation of $20.
a. Explain why you cannot determine the probability that the next customer will spend at least
$40.
b. Can you find the probability that the next 50 customers will spend an average of at least $40?
If so, find it!
4. The following are the heights in a class of 25 first-graders.
34
38
39
a.
42
37
39.5
41.2
40.3
36
44
39
34
39.7
37.2
38
40
41
38
36.5
35
35.5
34.7
36.8
Find a point estimate of the mean height for mean height of all first-graders.
b. Find a point estimate for the proportion of first-graders who are taller than 40 inches.
c.
Find a point estimate for the median height for all first-graders.
d. Find a point estimate for the standard deviation in the heights of all first-graders.
39
41
5. An insurance company checks police records on 582 accidents selected at random and notes that
teenagers were at the wheel in 91 of them. Create a 95% confidence interval for the percentage of all
auto accidents that involve teenage drivers.
6. A May 2002 Gallup Poll found that only 8% of a random sample of 1012 adults approved of attempts to
clone a human. Create a 92% confidence interval for the percentage of all adults who approve of
attempts to clone a human.
7. In 1998 a San Diego reproductive clinic reported 49 births to 207 women under the age of 40 who had
previously been unable to conceive. Find a 94% confidence interval for the success rate at this clinic.
Would it be misleading for the clinic to advertise a 25% success rate? Explain.
8. In preparing a report on the economy, we need to estimate the percentage of business that plan to hire
additional employees in the next 60 days. How many randomly selected employers must we contact in
order to create an estimate in which we are 98% confident with a margin of error of 5%?
9. It’s believed that as many as 25% of adults over 50 never graduated from high school. We wish to see
if this percentage is the same among the 25 to 30 age group. How many of this younger age group must
we survey in order to estimate the proportion on non-grads to within 6% with 90% confidence?
10. A newspaper reports that the governor’s approval rating stands at 65%. The article adds that the poll is
based on a random sample of 972 adults and has a margin of error of 2.5%. What level of confidence
did the pollsters use?