Grade 12 Applied Math Unit #2 Statistics Assignment #5 Binomial
Distribution
1. Are the following distributions normal approximations of binomial distributions? How do
you know?
a.
b.
c.
d.
60 trials where the probability of success on each trial is 0.05
60 trials where the probability of success on each trial is 0.20
600 trials where the probability of success on each trial is 0.05
80 trials where the probability of success on each trial is 0.99
2. Determine the mean and standard deviation for each binomial distribution. Assume that
each distribution is a reasonable approximation to a normal distribution.
a. 50 trials where the probability of success for each trial is 0.35
b. 44 trials where the probability of failure for each trial is 0.28
c. The probability of the Espro I engine failing in less than 50 000 km is 0.08. In
1998, 16 000 engines were produced. Find the mean and standard deviation for the
engines that did not fail.
Solve the following problems using binomial solutions.
3. The probability that a student owns a CD player is 3/5. If eight students are selected at
random, what is the probability that:
a. exactly four of them own a CD player?
b. all of them own a CD player?
c. none of them own a CD player?
4. The probability that a motorist will use a credit card for gas purchases at a large service
station on the Trans Canada Highway is 7/8. If eight cars pull up to the gas pumps, what
is the probability that:
a. seven of them will use a credit card?
b. four of them will use a credit card?
5. The manager of the Jean Shop knows that 3 percent of all jeans sold will be defective,
and the money paid for these pairs of jeans will be refunded. The manager went on
holidays for a period of time, and an employee sold 247 pairs of jeans. The employee
reported that refunds were given for 14 pairs of jeans.
a. What is the probability that 14 pairs of jeans were defective?
b. Does the employer have reason to be suspicious of the employee?
c. Does the employer have proof that the employee did something wrong?
6. A laboratory supply company breeds rats for lab testing. Assume that male and female
rats are equally likely to be born.
a.
b.
c.
d.
What is the probability that of 240 animals born, exactly 110 will be female?
What is the probability that of 240 animals born, 110 or more will be female?
What is the probability that of 240 animals born, 120 or more will be female?
Is it correct to say that, in the above situation, P(x ≥120) = P(x > 119), or do we
need to account for the values between 119 and 120?
7. A producer of hatching eggs acknowledges that 4 percent of all the eggs produced will
not hatch. In a shipment of 600 eggs, what is the probability that:
a. at least 25 will not hatch?
b. fewer than 20 will not hatch?
c. between 20 and 24 inclusive will not hatch?
8. It is known from past experience that, on average, 4.5 percent of all mouse traps
produced by a company are defective. If 50 traps produced by the company are selected
at random, find the probability that from 3 to 6 inclusive of them are defective.
9. In a small community, 65 percent of the people speak at least two languages. What is the
probability that, if a group of 40 people is randomly selected, at most seven of them
speak only one language?
Solve the following binomial problems as normal distribution problems
10. A laboratory supply company breeds rats for lab testing. Assume that male and female
rats are equally likely to be born.
a. What is the probability that of 240 animals born, 110 or more will be female?
b. What is the probability that of 240 animals born, 120 or more will be female?
c. Compare the above answers to #6b and #6c.
11. A toy manufacturer produces balloons that have a 3 percent defective rate. In a
shipment of 4000 balloons, what is the probability that:
a. fewer than 100 balloons will be defective?
b. between 100 and 130 balloons inclusive will be defective?
12. It is known from past experience that, on average, 4.5 percent of all mouse traps
produced by a company are defective. If 50 traps produced by the company are selected
at random, find the probability that from three to six inclusive of them are defective.