## Question

1) Bob is pursuing an Executive MBA, He has 12 courses (no prerequisites for any of them) from which to choose for 3 semesters in an academic year (Fall, Spring, and Summer)

a) How many ways can he choose four Fall Semester courses from the list for the year if the order matters?

b) How many ways can he choose four different courses if the order does not matter?

c) If he has chosen the first semester’s courses, how many ways can he choose four more courses for the second semester? Assume the order does not matter

2) A Private Practice Attorney usually has five clients per day. Over the years she has recorded the number of cancellations and used the data to estimate the probability of 0 through 5 cancellations per day. In the table below X = number of cancellations per day and P(X) = the probability of x cancellations.

X 0 1 2 3 4 5

P(X) 0.205 0.410 0.328 0.051 0.005 0.001

a) Compute the expected number of cancellations per day (to the nearest 2nd decimal)

b) Compute the standard deviation for the number of cancellations (to the nearest 2nd decimal).

c) What is the probability that there will be 3 or more cancellations in a day?

d) What is the probability that there will be 2 or fewer cancellations in a day?

3) In 2013 60% of all US Households still had a landline connection for their phone. If you called 11 households at random back then, what is the probability that:

a. Exactly three households responded on a landline.

b. Every household had a landline

c. More than 5 households had a landline

d. Fewer than 6 households do NOT have a landline

4) The life of an I-phone is normally distributed with a mean 3 years and standard deviation 6 months. The manufacturer will replace it if it breaks during the guarantee period.

a. If the manufacturer guarantees the I-phone for 2 years what fraction of the phones will he probably have to replace?

b. How long should the guarantee period be if the manufacturer does not want to replace more than 5% of the I-phones? (Round to the nearest month).

5) At a pharmacy an assistant has been measuring the time a customer waits in line. Over a long period of time the assistant has found the mean waiting time to be 8.2 minutes with a standard deviation of 4.3 minutes.

c. What is the probability that a random sample of 36 customers will have a sample mean waiting time of 9 or more minutes?

d. What is the probability that a random sample of 49 customers will have a sample mean waiting time of less then 7 minutes?

6) A preliminary study at a chicken farm showed that for 35 chickens selected the mean weight was 2.5 pounds with a standard deviation 0.8 pound (sample is normally distributed).

e. Find a 95% confidence interval (to the nearest tenth) for the population mean weight of the chickens.

f. How many more chickens should be included in the sample if we want to say with 99% confidence that the population mean weight of the chickens is within 0.1 pound of the sample mean.

## Solution Preview

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1)The following questions deal with counting techniques which is usually taught by example as there isn’t a ton of theory behind the concepts. To prove my solutions using the induction principle, I’ll use an example of three balls numbered 1,2, and 3.

A) 12!=479,001,600

If we have to order our three balls then these are the following possible sets: {1,2,3},{1,3,2},{2,1,3},{2,3,1},{3,1,2},{3,2,1}. We can count these six sets using 3!=3*2*1=6.

B) 12*11*10*9=11,880

For this problem, the orders of our sets are irrelevant. For example, if the classes are lettered A,B,…,L, then {A,B,C}={C,B,A}. Essentially we “use up” a class with each pick.

C) 8!=40,320

If we have already used up {A,B,C,D}, then we’re left with {E,F,…,L} which is computed using a similar technique to 1A....

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