a.
If the rate of calls is actually 20 per hour, what is the probability that 9 or more calls will come in during a given 15-minute
period?
b.
If the rate of calls is really 30 per hour, what is the probability that 9 or more calls will come in during a given 15-minute period?
Homework 4- due Sunday, March 6
1.
A wildlife biologist examines frogs for a genetic trait he suspects may be linked to sensitivity to industrial toxins. Previously
research had established that his trait is usually found in 10% of frogs. He collects 13 frogs.
a. What probability distribution describes the number of frogs in the sample with this trait? Check conditions
b. If the frequency of the trait has not changed, what is the probability he finds the trait
(i) no one of the 13 frogs
(ii) at least 1 but fewer than 4 frogs.
c.Find the expected number of frogs in the sample with this trait. Calculate the standard deviation.
d.Suppose the actual number of frogs in the sample with this trait is equal to 4.Is there any evidence to suggest that this trait is found
in more than 10% of frogs? Justify your answer.
2.Tay- Sachs disease is a genetic disorder that is usually fatal in young children. If both parents are carriers of the disease, the probability that their offspring will develop the disease is approximately 0.25.Suppose a husband and wife are both carriers of the disease and the wife is pregnant on three different occasions. If the occurrence of Tay-Sachs in any one offspring is independent of the occurrence in any other, what are the probabilities of these events: a.
All three children will develop Tay-Sachs disease.
b .Only one child will develop Tay-Sachs disease.
c.
The third child will develop Tay-Sachs disease, given that the first two did not.
3. Bender Electronics buys keyboards for its computers from another company. The keyboards are received in shipments of 100
boxes, each box containing 20 keyboards. The quality control department at Bender Electronics first randomly selects one box from
each shipment and then randomly selects 5 key boards from that box. The shipment is accepted if not more than 1 of the 5
keyboards is defective. The quality control inspector at Bender Electronics selected a box from a recently received shipment of key-
boards. Unknown to the inspector, this box contains 6 defective keyboards.
a.
What is the probability that this shipment will be accepted?
b.
What is the probability that this shipment will not be accepted?
4. York Steel Corporation produces a special bearing that must meet rigid specifications. When the production process is running
properly, 10% of the bearings fail to meet the required specifications. Sometimes problems develop with the production process
that cause the rejection rate to exceed 10%. To guard against this higher rejection rate, samples of 15 bearings are taken periodically
and carefully inspected. If more than 2 bearings in a sample of 15 fail to meet the required specifications, production is suspended
for
necessary adjustments.
a
.
a.If the true rate of rejection is 10% (that is, the production process is working properly), what is the probability that the
production
will be suspended based on a sample of 15 bearings?
b
.
b.What assumptions did you make in part a?
5.
The number of calls that come into a small mail-order company follows a Poisson distribution. Currently, these calls are serviced
by
a single operator. The manager knows from past experience that an additional operator will be needed if the rate of calls
exceeds
20 per hour. The manager observes that 9 calls came into the mail-order company during a randomly selected 15-min c.
Based on the calculations in parts a and b, do you think that the rate of incoming calls is more likely to be 20 or 30 per hour?
d.
Would you advise the manager to hire a second operator? Explain.
6.
A history teacher has given her class a list of seven essay questions to study before the next test. The teacher announced that she
will choose four of the seven questions to give on the test, and each student will have to answer three of those four questions.
Suppose that a student has enough time to study only five questions. What is the probability that the student will have to answer a
question that he or she did not study? That is, what is the probability that the four questions on the test will include both questions
that the student did not study?
