Quantitative Analysis Quiz #1

Basic Probability

1.

Quantity DemandedNumber of Customers

103

205

307

403

502

Total20

A. Determine the expected value of the demand? EV(x)= 28

B. What is the standard deviation for this data? Standard Deviation = 11.667

2.

You have a deck of 52 playing cards, find the following probabilities.

  1. What is the probability of drawing a five of clubs? 1/52
  2. What is the probability of drawing a diamond or a spade? 26/52
  3. What is the probability of drawing a King or a heart? 16/52
  4. Drawing two cards, what is the probability of drawing a face card and a three? 16/52 x 4/52 = .01923

3.

You have 3 red balls, 11 green balls and 6 white balls in a basket. A ball is drawn

and replaced, and then a second ball is drawn.

  1. What is the probability of drawing a green ball on both draws?

.55 x .55 = .3025

  1. What is the probability of drawing a white ball first, then a green ball?

.30 x .55 = .1650

  1. What is the probability of drawing a red ball second given the first ball was white? .30 (since these are independent events, the first draw has no impact on the second draw)

4.

There is an 80% chance that it will rain today. Your professor said there is a 60% chance that you will go to the park for class today. What is the probability that

you will go to the park and it rains? .80 x .60 = .48

5.

Seven out of ten people taking the new professor’s class like it. There are 200 students at the school, but only 50 are allowed in his class. You survey students at the school about the new teacher.

  1. What is the probability you survey a student not taking the class?

150/200 = .75

  1. What is the probability you survey a student taking the class who does not like the professor? 50/200 x 3/10 = .075

6.

The New Wave Bicycle shop sells 120 bicycle a month on average with a

standard deviation of 15. Their sales are approximately normally distributed.

Using Appendix A:

  1. What is the probability they will sell more than 150 bicycles in a month?
  2. What is the probability they will sell less than 105 bicycles in a month?
  3. What is the probability they will sell between 105 and 135 bicycles in a month?

Solutions:

A. Z= (150-120)/ 15 = 2 Table Lookup .97725 1-.97725 = .02275

B. Z= (105-120)/ 15 = -1 Table Lookup .84134 1-.84134 = .15866

C. Z= (105-120)/ 15 = -1 Z= (135-120)/ 15 = 1 Lookup answer .68268

7.

Students arrive at the campus clinic at an average rate of 3 per hour. The demand

at the clinic follows a Poisson distribution.

  1. What is the mean of the distribution? Lambda = 3
  2. What is the variance of the distribution? Variance = 3
  1. What is the probability that exactly 2 students arrive per hour?

P(x=2) = X e’lambda/X! = 3^2(.0498)/2 = .2241