Statistics

MSB 701

Quiz 1, Lehman College SP2021

Professor Masele Kibassa

Please show all work/calculations to receive credits

1. (For 20 points) Given the following table of a random variable X and corresponding probabilities:

X	P(X)
2	.01
3	.35
4	c
5	.10
6	.15
7	.20

a. What should c be for this to be a probability distribution of X?

b. Compute the mean or expected value

c. Compute the variance

d. Compute the standard deviation

2. (For 20 points ) Joseph would like to buy a new suit. The cost of suits is known to be normal, with a mean of $175 and a standard deviation of $23. If he is to purchase one suit:

Please show all work and provide Normal curve illustrations

a. What is the probability that it will cost less than $147?

b. What is the probability that is will cost more than $ 139?

c. What is the probability that it will cost between $ 160 and $ 200?

d. What costs separate the middle 75 % of all suits from the rest of the suits?

e. What cost separates the top 7 % of all suits from the rest of the suits?

3. (For 20 points ) If the following information is given about a specific company

Selling price per unit $ 51.25

Fixed Expenses

Selling and Administration $ 77,050

Interest Expenses $ 34,250

Variable Expenses

Cost of Goods Sold $18.35

Selling and Administrative $ 13.29

a. What is the company’s contribution margin? What does it mean?

b. How many items the company must sell in order to break even? What is it in dollars term?

c. At the end of the month, instead of breaking even, the company registered a loss of $22345, what number of units were sold?

d. At the end of the month, instead of breaking even, the company registered a profit that is 70% of Interest expenses amount, what number of units were sold?

4. (For 20 points ) Sixty-three percent of adults would still consider a car brand despite product/safety recalls. You randomly select 11 adults. Use binomial distribution to find the probability that the number of adults who would still consider a car brand despite product/safety recalls is:

Please show all work/calculations to receive credits

a. Exactly 3

b. At most 3

c. At least 3

d. Between 2 and 5, inclusive

5. (For 20 points ) In your own words , please define quantitative analysis, and elaborate the quantitative analysis process. (You have the entire page; be as detailed as possible)