6. A calculus exam had a mean of 75 and a
standard deviation of 6. If Sally had made a 78
on this exam, what is her z-score?
16. Find the following probabilities:
b. P1.68 Z 2.09
c. PZ 0.56
d. P0.52 Z 0.52
e. P2.09 Z 1.32
f. PZ 1.08
a. P Z 1.82
18. Find the value of c that satisfies each of the
following probabilities:
0.0495
b. PZ c0.8438
c. PZ c0.0778
d. Pc Z c0.9774
a. P Z c
4.4
2. The mean TOEFL score of international
students at a certain university is normally
distributed with a mean of 490 and a standard
deviation of 80. Suppose groups of 30 students
are studied. Find the mean and the standard
deviation for the distribution of sample means.
5. A waiter estimates that his average tip per
table is $20 with a standard deviation of $4. If
we take samples of 9 tables at a time, calculate
the following probabilities when the tip per table
is normally distributed.
a. What is the probability that the average
tip for one table is less than $21?
b. What is the probability that the average
tip for one table is more than $21?
c. What is the probability that the average
tip for one table is between $19 and $21?
12. In a large population, 76% of the households
own microwaves. A simple random sample of
100 households is to be contacted and the sample
proportion computed. What is the mean and
standard deviation of the sampling distribution of
the sample proportions?