1. Vehicle speeds at a certain highway location are believed to

1. Vehicle speeds at a certain highway location are believed to be approximately normally
distributed with a mean of 60 mph and standard deviation of 6 mph. For each of the following
questions, fill in the blank with the appropriate speeds. Apply the Empirical Rule.
a. One vehicle is randomly selected; there is about a 68% that the vehicle’s speed will
be between ___ and ___.

b. One vehicle is randomly selected; there is about a 95% chance that the vehicle’s
speed will be between ___ and ___.

c. The speeds of randomly selected samples of 16 vehicles will be recorded. For
samples of
vehicles, there is about a 68% chance that a sample’s mean speed

n 16

will be between ___ and ___.

d. The speeds of randomly selected samples of 36 vehicles will be recorded. For
samples of
vehicles, there is about a 95% chance that a sample’s mean speed

n 36

will be between ___ and ___.

e. The speeds of one randomly selected sample of 36 vehicles were recorded. The
sample mean
was 57 mph. What is the probability, given
and
, that

60

x

a sample of

n 36

6

would have a mean of 57 mph or less?

f. Given your results from part (e), do you think it is likely that this sample of 36
vehicles came from a population with
? Why or why not?

60

2. Suppose that a team of Penn State medical researchers wanted to estimate the true
proportion of all teenagers with high blood pressure whose blood pressure decreases after
taking calcium supplements. To test this, they plan a clinical trial in which 200 teenagers with
high blood pressure were given calcium supplements. Of the 200 participants, 120
experienced a decrease in blood pressure.
a. Compute

b. Compute

µ
p

SE ( µ )
p

using

µ
p

as an estimate of p

c. Verify that it is appropriate to use normal approximation methods with the data
from this study.

d. A pharmaceutical company claimed that calcium supplements decrease blood
pressure in 64% of all teenagers with high blood pressure. What is the probability that
a population where
would produce a random sample of
with a

p 0.64

n 200

sample proportion as low (or lower) than the one found in this sample?

e. Given your results from part (d), do you think that the pharmaceutical company’s
claim that the population proportion is .64 could be accurate? Or, do you think that
their claim is an overestimate of the true effectiveness of calcium supplements for
reducing blood pressure in teens? Why?