Exam # 3 Review
§Chapter 4.
1. An eight-sided die is rolled 500 times. Below is the frequency distribution for the value of the roll x.
x 1 2 3 4 5 6 7 8
f 74 64 62 68 67 65 45 55
Write a probability distribution for x, make a histogram, and find the
mean, variance, and standard deviation.
2. There are three tosses of a fail coin. The random variable x is the
number of heads. Write down the probability distribution, and find
the mean, variance, and standard deviation for the number of heads.
3. The value of two investments x and y are subject to three economic
conditions: a recession, stable economy, and growing economy.
Economy Probability Investment x Investment y
Recession
0.2
-$100
-$200
Stable
0.5
+$100
+$50
Growth
0.3
+$250
$350
Find the expected value for each investment. Calculate the standard
deviation for each investment.
4. Select a card at random from a standard deck of cards. Note if the card
is a face card (jack, queen, king, or ace) and put it back and shuffle
the deck. You perform this experiment 6 times. The random variable
is the total number of face cards. Why is this binomial?
Construct the probability distribution, and histogram.
5. You are pretty good at a dentist simulator on your smartphone. You
basically have a 82% chance of a successful root canal. You perform
281 root canals in the next month. The binomial random variable x is
the number of successful root canals. What is its mean, variance, and
standard deviation?
6. Salt Lake City has about a 32.9% chance a day to rain in June. Write
the binomial probability distribution for x the number of rainly days
over seven days in June. Graph the histogram.
7. A social network website defines success if a web surfer stays logged on
for more than 10 minutes. Suppose the probabilitiy that a web surfer
stays on for more than 10 minutes is 0.262. The next five web surfers
visit the site. What is the probability that:
(a) No web surfers stay on for more than 10 minutes. (b) At least 1
web surfer stays on for more than 10 minutes? (c) All five visitors stay
on for more than 10 minutes.
§Chapter 5.
1. Draw the normal curves for a normal distribution with:
(a) µ = 3 and σ = 1.8 (b) µ = 6.15 and σ = 0.05 (c) µ = 73 and σ = 8
2. Find the z-score for the following normal random variable values.
(a) x = 1.65 for µ = 3 and σ = 1.8 (b) x = 6.206 for µ = 6.15 and
σ = 0.05 (c) x = 91 for µ = 73 and σ = 8
3. For the standard normal curve, find the areas below the curve and
(a) to the right of z = 0.25 (b) to the left of z = −0.25 (c) in between
z = 0.00 and z = 0.25 (d) in between z = −2.00 and z = 2.00.
4. SAT writing scores follow a normal distribution with a mean of 493
and standard deviation 111.
(a) What percent of SAT writing scores are less than 600? (b) If 1000
SAT writing scores are randomly selected, about how many of them
would you expect to be greater than 600?
5. SAT math scores follow a normal distribution with a mean of 515 and
standard deviation 116.
(a) What percent of SAT math scores are less than 500? (b) If 1500
SAT math scores are randomly selected, about how many would you
expect to be greater than 600?
6. Use the standard normal distribution table to find the percentiles for
(a) 42% (b) 75% (c) 95%
7. The heights of women are approximately normally distributed with a
mean of 64.3 inches and standard deviation 2.6 inches.
(a) What height corresponds to the 90th percentile? (b) What height
represents the first quartile?
8. The heights of men are approximately normally distributed with a
mean of 69.9 inches and standard deviation 3.0 inches.
(a) What height corresponds to the 95th percentile? (b) What height
represents the first quartile?