Quantitative Business Methods Hw 4

MA218 Classwork 4 1. A survey was given to 4000 adults (18 or older) about whether or not they have auto insurance. Here are the results:

Ages YES NO

18 to 34 1500 340

35 and older 1900 260

A. What is the probability that a randomly selected person does not have insurance? B. What is the probability that a randomly selected person between the ages of 18 and 34 does not

have insurance? C. What is the probability that a randomly selected person who is 35 or older does not have

insurance? D. What is the probability that a randomly selected adult is between 18 and 34 years old? E. Frank is one of the people in the survey that does not have auto insurance. What is the

probability that Frank is between 18 and 34? 2. During a recent year, speeding was reported in 12.9% of all automobile accidents in the United States. Assume the probability that speeding is reported in an accident is 0.129, the probability of an accident in which speeding is reported leading to a fatality is 0.196, and the probability of an accident in which speeding is not reported leading to a fatality is 0.05. Suppose you learn of an accident involving a fatality. What is the probability that speeding was reported? 3. a) An oil company purchased an option on land in Alaska. Preliminary geologic studies as- signed the following prior probabilities.

P(high quality oil) = 0.50 P(medium quality oil) = 0.20

P(no oil) = 0.30 What is the probability of finding oil? b) After 200 feet of drilling on the first well, a soil test is made. The probabilities of finding the particular type of soil identified by the test are

P(soil | high quality oil) = 0.20 P(soil | medium quality oil) = 0.20

P(soil | no oil) = 0.30 How should the firm interpret the soil test? What is the new probability of finding oil?

MA 218 Classwork 5

1) The following table gives child birth data for the number of children born in individual pregnancies in

both 1996 and 2006.

# of children 1996 Frequency 2006 Frequency Single child 3,671,455 3,971,276 Twins 100,750 137,085 Triplets 5,298 6,118 Quadruplets 560 355 Quintuplets or more 81 67

a) Let X be a random variable that represents the number of children born in a single pregnancy in 1996.

(Let X=5 represent 5 or more) Find P(X=1), P(X=2), P(X=3), P(X=4), and P(X=5).

b) Compute E[X]

c) Let Y be a random variable that represents the number of children born in a single pregnancy in 2006.

(Let Y=5 represent 5 or more) Find P(Y=1), P(Y=2), P(Y=3), P(Y=4), and P(Y=5).

d) Compute E[Y]

e) There has been a hypothesis that more women are having multiple births due to increased use of

fertility drugs. Does your data from above support this hypothesis? Explain.

2) A recent survey asked randomly selected Americans if they had a positive view of the car company

Tesla. The survey found that 81% of Americans hold a positive view of the company.

a) In a sample of six randomly chosen Americans, what is the probability that ​exactly​ 2 have a positive view of Tesla?

b) In a sample of six randomly chosen Americans, what is the probability that ​at least​ 2 have a positive view of Tesla?

c) In a sample of six randomly chosen Americans, what is the probability that ​none​ have a positive view of Tesla?

d) Did any of the results above surprise you? How do they compare with the general 81% number?

Explain

3) Airline passengers arrive randomly and independently at the check in counter at a large airport with

lots of flights. The airline is interested in knowing the probability of having a very crowded check in desk.

On average, 10 customers per minute arrive at the check in desk.

a) What is the probability of having no arrivals in a one minute period?

b) What is the probability of having 3 or fewer arrivals in a one minute period?

c) What is the probability of having 20 or more arrivals in a one minute period?

d) Is it more likely that the desk will have no arrivals or greater than 20? Given this information, how

would you determine staffing levels for the ticket desk?