Download 5.3-5.4-Review - Bryant Middle School

Statistics
5.3 & 5.4 Review
Name: ___________________________
1. The ACT has a mean of 21 and a standard deviation of 3.5.
a) Find the probability that a student chosen at random scored more than 24 on the ACT.
b) Find the probability that in a sample of 35 students, the mean ACT score is more than 24.
c) Which is more likely to happen? Part (a) or part (b)? Explain.
2. The distribution of room and board expenses per year at a 4-year college is normally
distributed with a mean of $5850 and a standard deviation of $1125. Random samples of size 20
are drawn from this population and the mean of each sample is determined. Which of the
following mean expenses would be considered unusual? Explain using z-scores or probability.
A) $5180
B) $6180
C) $6350
D) none of these
3. Assume that the heights of men are normally distributed with a mean of 69.0 inches and a
standard deviation of 2.8 inches. Find the probability that a man chosen at random is less than
72 inches tall.
4. Assume that the heights of men are normally distributed with a mean of 69.0 inches and a
standard deviation of 2.8 inches. If 64 men are selected randomly, find the probability that they
have a mean height greater than 68.9 inches.
5. Assume that the heights of men are normally distributed with a mean of 69.0 inches and a
standard deviation of 2.8 inches. If 50 men are randomly selected, find the probability that they
have a mean height between 68 and 70 inches.
6. Assume that blood pressure readings are normally distributed with a mean of 116 and a
standard deviation of 4.8. Find the probability that a person chosen at random will have a blood
pressure less than 118.
7. Assume that blood pressure readings are normally distributed with a mean of 116 and a
standard deviation of 4.8. If 36 people are randomly selected, find the probability that their
mean blood pressure will be less than 118.
8. A soda machine dispenses normally distributed amounts of soda with a mean of 20 ounces
and a standard deviation of 0.2 ounce. Are you more likely to randomly select one bottle with
more than 20.3 ounces or are you more likely to select a sample of 8 bottles with a mean amount
of more than 20.3 ounces? Explain.
9. IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. Find
the probability of choosing a person at random whose IQ score is greater than 106.
10. IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. You
take a sample size of 75. What is the probability that the mean IQ score for the sample is
between 95 and 106?