MATH 17282-Suppose that 20% of the adult women in the

Suppose that 20% of the adult women in the

United States dye or highlight their hair. We

would like to know the probability that a SRS of

size 200 would come within plus or minus 3

percentage points of this true value. In other

words, find probability that ˆp takes a value

between 0.17 and 0.23

Use the following to answer questions 12 - 13: The high temperature in Chicago for the month of August is
approximately normally distributed with mean ? = 80 F and standard deviation = 8 F. Suppose we take
a SRS of 16 days in August and want to determine the sample mean, ¯x high temperature.
12. What is the standard deviation (standard error) of the sample mean high temperature.
a. 8
b. 2
c. 0.5
d. 10
e. 20
13. What is the probability that a random sample of 16 days in August have a sample mean high temperature
of at least 82 F?
a. 0.5987
b. 0.2500
c. 0.1587
d. 0.8413
e. Cannot be determined.

3. If a distribution has a mean of 48 and standard deviation of 3.2, what is the value that corresponds to
a z-score of -1.6?
a. 38.22
b. 42.88
c. 53.12
d. 46.40
e. none of these