Practice Quiz Week 6 - Math 221 Quiz Review for Weeks 5 and...

Math 221
Quiz Review for Weeks 5 and 6
1. Find the area under the standard normal curve between z = 1.6 and z = 2.6.
2. A business wants to estimate the true mean annual income of its customers. It
randomly samples 220 of its customers. The mean annual income was $61,400
with a standard deviation of $2,200. Find a 95% confidence interval for the true
mean annual income of the business’ customers.
3. IQ test scores are normally distributed with a mean of 100 and a standard
deviation of 15. An individual's IQ score is found to be 120. Find the z-score
corresponding to this value.
4. Two high school students took equivalent language tests, one in German and one
in French. The student taking the German test, for which the mean was 66 and the
standard deviation was 8, scored an 82, while the student taking the French test,
for which the mean was 27 and the standard deviation was 5, scored a 35.
Compare the scores.
5. A business wants to estimate the true mean annual income of its customers. The
business needs to be within $250 of the true mean. The business estimates the
true population standard deviation is around $2,400. If the confidence level is
90%, find the required sample size in order to meet the desired accuracy.
6. The distribution of cholesterol levels in teenage boys is approximately normal
with mean = 170 and standard deviation = 30 (Source: U.S. National Center for
Health Statistics). Levels above 200 warrant attention. Find the probability that a
teenage boy has a cholesterol level greater than 200.
7. An airline knows from experience that the distribution of the number of suitcases
that get lost each week on a certain route is approximately normal with mean =
15.5 and standard deviation = 3.6. What is the probability that during a given
week the airline will lose between 10 and 20 suitcases?
8. An automobile safety engineer wants to estimate the mean cost to repair a Chevy
Corvette involved in a 30 mile per hour head-on collision. The engineer crashes
24 Corvettes and finds the mean damage is $11,500 with a standard deviation of
$2,700. Find a 98% confidence interval for the true mean cost to repair this type
of car.
9. A competency test has scores with a mean of 80 and a standard deviation of 10. A
histogram of the data shows that the distribution is normal. Use the Empirical
Rule to find the percentage of scores between 70 and 90.

10. An auditor wants to estimate what proportion of a bank’s commercial loan files
are incomplete. The auditor wants to be within 11% of the true proportion when
using a 90% confidence level. How many files must the auditor sample? No