**Quantitative Foundation for Engineering Managers**

**PRE – COURSE QUIZ**

Formula Sheet With the Z- table

**1. You are dealt a king from a standard deck of cards. What is the probability that the next card you are dealt will be a jack? (Both cards come from the same 52 card deck with 4 each of aces, kings, queens, jacks and the numbers 2-10.)**

a. 4/52

b. 3/52

c. 4/51

d. 3/51

**2. A bag of marbles contains 24 marbles: 5 red marbles, 6 white marbles, 8 yellow marbles and 5 green marbles. What is the probability of drawing a green marble and then a yellow one (without putting the green one back)?**

a. 5/24 + 6/24

b. 5/24 + 6/23

c. 5/24 x 6/24

d. 5/24 x 6/23

**3. A warehouse ships a package for an order. The probability that the order was correctly packaged is 85%. The probability that the package will be delivered on or before the specified delivery date is 67%. What is the probability that the patient receives a correct package within the specified delivery time?**

a. 57%

b. 52%

c. 67%

d. 76%

**4. The time to assemble a product follows a normal distribution with an average of 28 minutes and standard deviation of 2.0 minutes. The proportion of time that the assembly takes longer than 30 minutes to assemble is**

a. 0.8413

b. 0.1587

c. 0.2048

d. 0.3271

5. **Which of the following is not true of the binomial distribution?**

a. The outcome of each trial can only be success or failure

b. The probability of a success is constant.

c. The probability of drawing a club from a standard deck of cards can be determined with the binomial distribution

d. Probabilities associated with successive flips of a coin can be analyzed with the binomial distribution.

6. **Customer arrival rates follow a Poisson distribution. Customers arrive at a store at an average of 8 per hour. What is the probability that exactly 10 customers will arrive in an hour?**

a. 0.099

b. 0.200

c. 0.156

d. 0.123

**7. At a popular restaurant, during the dinner hours, the average time to wait for a table is 25 minutes. Assuming an exponential distribution what is the probability of being seated in less than 15 minutes after you arrive?**

a. 50.0%

b. 45.1%

c. 28.2%

d. 57.3%

**8. A sample of size 16 is taken from a process and the mean and standard deviation of the sample observations are calculated a 10.50 and 1.23 respectively. To determine the 95% confidence interval for the mean, which distribution should be used?**

a. Normal distribution

b. t distribution

c. F distribution

d. Chi-squared distribution

**9. Two machines are being considered for processing a critical component. Samples were taken from both machines:**

** Sample size Sample mean Sample standard deviation**

** Machine A 21 0.99 0.34**

** Machine B 25 1.03 0.45**

**A hypothesis test will be used to test the hypothesis that the variance of Machine B is greater than the mean of A with 95% confidence. **

**The type of test which would be used to test the hypothesis is**

a. 2 sample t test

b. 2 sample Z test

c. F test

d. Chi squared test for proportions

**10. A simple linear regression was performed on a set of data and resulted in the equation y=-2x+30. The associated correlation coefficient, was determined to be r= -0.87. Which of the following is true of this analysis?**

a. A calculation error has occurred as the correlation coefficient cannot be negative.

b. The r value is negative because as the x variable increases, the y variable also increases.

c. The relationship between variables x and y would be considered rather strong.

d. None of the above.