PRACTICE TEST #1
1. Diabetes patients are classified by gender and type of diabetes (I or II).
Type I Diabetes
Type II Diabetes
Male
35
24
Female
44
22
If one file is selected at random, find the probability that
A) the selected individual is female
B) the selected individual is Type II
2. The American Red Cross says that about 45% of the US population has type O blood,
40% type A, 11% type B, and the rest type AB. Someone volunteers to give blood. What
is the probability that this donor:
A) has type AB blood
B) has type A or type B blood
C) is not type O
3. The weight of potato chips in a medium-size bag is stated to be 10 ounces. The
amount that the packaging machine puts in these bags is believed to have a Normal
distribution with a mean of 10.2 ounces and a standard deviation of 0.12 ounces.
A) What fraction of all the bags sold are underweight?
B) What’s the probability that the mean weight of 3 bags is below the stated amount?
C) What’s the probability that the mean weight of a 24-bag case is below 10 ounces?
D) How heavy are the 10% heaviest 24-bag cases?
4. Random Numbers: A number is picked at random from between 2 and 10. Draw a
picture of the probability density function, give its height, shade in the area that
corresponds to finding the probability the number is at least 7.5, and give that probability.
5. Sampling: In a population of size 11 with a mean of 9.5 and a standard deviation of 5.0
all 214358881 samples of size 8 are taken.
A) What is the mean of all the sample means?
B) What is the standard deviation of all the sample means?
6. Medicine: In order to test a new drug for adverse reactions, the drug was administered
to 1200 test subjects with the following results: 70 reported that their only adverse
reaction was loss of appetite, 120 reported only loss of sleep, and 800 reported no adverse
reactions.
A) If a randomly selected test subject suffered loss of appetite, what is the probability that
the subject also suffered loss of sleep?
B) If a randomly selected test subject suffered loss of sleep, what is the probability that
the subject also suffered loss of appetite?
C) If a randomly selected test subject did not suffer a loss of appetite, what is the
probability that the subject suffered loss of sleep?
D) If a randomly selected test subject did not suffer loss of sleep, what is the probability
that the subject suffered a loss of appetite?
7. Politics: In a given county records show that of the registered voters, 45% are
Democrats, 35% are Republicans, and 20% are Independents. In an election, 70% of the
Democrats, 40% of the Republicans, and 80% of the Independents voted in favor a parks
and recreation bond proposal. If a registered voter chosen at random is found to have
voted in favor of the bond:
A) What is the probability that the voter is a Republican?
B) What is the probability that the voter is a Democrat?
C) What is the probability that the voter is an Independent?
8. In a survey of subscribers of Fortune Magazine, 72% rented a car for either personal or
business reasons in the last 12 months, 54% rented a car for business reasons, 51% for
personal reasons.
A) What is the probability a subscriber rented a car for business reasons and personal
reasons?
B) What is the probability a subscriber did not rent a car in the last 12 months?
C) What is the probability a subscriber rented a car for business reasons only in the last
12 months?
9. During the winter Moe experiences difficulty in starting his two cars. The probability
the first car starts is 0.85 and the probability the second car starts is 0.60. There is a 0.48
probability that both start.
A) What is the probability that at least one car starts?
B) What is the probability that neither starts?
10. A survey of automobile ownership was conducted for 200 families in Denver. The
results of the study showing ownership of automobiles of US and foreign manufacturers
follows:
Own a US car
Do not own a US
Totals
car
Own a foreign car
28
9
37
Do not own a
155
8
163
foreign car
Totals
183
17
200
A) What is the probability that a family owns both a US and a foreign car?
B) What is the probability that a family owns a car, US or foreign?
C) If a family owns a US car, what is the probability it also owns a foreign car?
D) If a family owns a foreign car, what is the probability it also owns a US car?
E) Are US and foreign car ownership independent? Explain.
11. RV means/variance: Suppose population X has a mean of 10 and a variance of 6,
while population Y has a mean of 8 and a variance of 4.
A) Suppose 2 is added to each data from X, what will be the new mean and variance?
B) Suppose we take one data from X and one from Y and subtract and do this all possible
ways, what will be the mean and variance of the random process?
C) Suppose all the data from X is divided by 5, what will be the new mean and variance?
12. Suppose the heights of kindergarten children can be described by a Normal model
with a mean of 38.6 inches and a standard deviation of 1.9 inches.
A) What fraction of kindergarten would you expect to be less than 3 feet tall?
B) In what height interval would you expect to find the middle 80% of the
kindergarteners?
C) At least how tall are the tallest 10%?
D) What percent are taller than 39 inches?