b.
What is the probability that a random sample of 40 farms has a mean cotton yield of at least 400 pounds?
.

5.
Suppose that the makers of Wal-Mart’s Dr. Thunder believe that its taste is equally preferred to Dr. Pepper.
Being a skeptic of this claim, you take a random sample of 80 people and administer a taste test to determine
which drink they prefer.
If they are indeed equally preferable, what is the probability that fewer than 40% of the
people in the sample prefer Dr. Thunder?
0

6.
For a student to graduate, a high school requires that each student demonstrate competence in mathematics by
scoring 70 or above on a mathematics achievement test.
The scores of those students taking the test are
normally distributed with a mean of 75 and a standard deviation of 7.3.
X = mathematics achievement test score
X is normal with
µ
= 75 and
σ
= 7.3
a.
If one senior takes the test, find the probability that he or she scores between 72 and 79.
If the probability
cannot be found, explain why.

b.
Find the 35th percentile for the mathematics achievement test.

c.
What is the probability that in a senior class of size 108 the average score is greater than 76?

Exam 3 Supplemental Problems Solutions
7.
The lengths of human pregnancies from conception to birth have a mean of 266 days and a standard deviation
of 16 days.
Find the following.
X = pregnancy length
distribution of X is unknown (assume not normal),
µ
= 266,
σ
= 16
a.
The probability that a woman’s pregnancy will last longer than 290 days.

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3
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6

b.
The mean for the sampling distribution of the sample mean for a sample of 36 pregnant women.