Part B - Free Response Questions (Show your work for each problem)(60 points)

Q1.

(a). Suppose you set up a new IRA(Individual Retirement Account) that pays an APR of 5.1% compounded monthly. If you contribute $150 per month for 15 years, how much will the IRA contain at the end of that time? ( 5 points)

Soln.

(b).Brandi deposits $75 at the end of each month into an account with APR of 7% for 10 years. Assume the payment period is the same as the compounding period. How much will the account contain at the end of that period? How much did Brandi deposit? ( 5 points)

Soln.

Q2.

(a).Suppose you have just obtained a 30 - year home mortgage in the amount of $74,000 at an APR of 4.3%. Find the required monthly payment and also the monthly payment that you would need to make to pay off the loan in 20 years. How much would you save in interest charges by paying off the loan in 20 years? ( 5 points)

Soln.

(b).Suppose you have a balance of $6400 on your credit card, which charges an APR of 24%. Assume that you charge no additional expenses to the card and you want to pay it off in 2 years of monthly payments. What is the total amount of interest you will end up paying? ( 5 points)

Soln.

Q3.

(a).Name the population.

A survey of 1200 New York City residents found that 35% own their own vehicle.

Soln.

(b). Name the sample. ( 2.5 points)

A survey of 1200 New York City residents found that 35% own their own vehicle.

Soln.

(c).Name the parameter. ( 2.5 points)

In a survey of 550 residents of rural Virginia, the average number of vehicles per household is 2.7.

Soln.

(d). Name the statistic. ( 2.5 points)

In a survey of 550 residents of rural Virginia, the average number of vehicles per household is 2.7.

Soln.

Q4.

Consider the following quiz grades for 22 students in an Introductory Statistics class.

88 96 9872 55 78 84 8792 73 4732 66 78 9486 89 9033 67 92 87

(a). Is the above data qualitative or quantitative? ( 3 points)

Soln.

(b).Make a frequency distribution for the above data using 10 - point bins. In your frequency distribution, include the relative frequency and the cumulative frequency.

( 7 points)

Soln.

Q5.

Consider a random sample of 20 concentrations of calcium carbonate (CaCo₃) in milligrams per liter.

130 129 131131 129 132 131 127 127 133

132 134 131 133 129 131 128 132 132 131

(a). What is the mean concentration? ( 2 points)

Soln.

(b).What is the median concentration? ( 1 point )

Soln.

(c).What is the mode of the concentration? ( 1 point)

Soln.

(d).Find the first quartile(Q₁) and the third Quartile(Q₃) of the above data and use the 1.5IQR rule to determine if there are any outliers in the data. ( 6 points)

Soln.

Q6.

Medical research has shown that a certain type of chemotherapy is successful 70% of the time when used to treat skin cancer. Suppose five skin cancer patients are treated with this type of chemotherapy and let X equal the number of successful cures out of the five. The probability distribution for the number X of successful cures out of the five is given in the following table.

X	0	1	2	3	4	5
P(X)	0.002	K	0.132	0.309	0.360	0.168

(a).Find the value of K ( 2 points)

Soln.

(b).Is this a valid discrete probability distribution? ( 2 points)

Soln.

(c).What is the probability of getting at least four cured patients? ( 2 points)

Soln.

(d). What is the probability of getting at most four cured patients? ( 4 points)

Soln.