**6. **(TCO 6) Assuming that the data are normally distributed with a mean of 45 and a standard deviation of 3.25, what is the z-score for a value of 40? (Points : 6)

**10. **(TCO 4) A jar contains balls of four different colors; red, blue, yellow and green. The total balls are divided as 40% red, 30% blue, 20% yellow, and 10% green. If you are to select one ball at random. Find the expected value of your winning amount if the payments are set to be $5, $10, $20, $50 for red, blue, yellow and green ball respectively.

Winning amount

5

10

20

50

Probability

40%

30%

20%

10%

**11. **(TCO 3) The grades of 20 students are listed in the stem and leaf diagram below. What is the probability of randomly selected student to have a grade more than or equal to 60 and less than or equal to 80.

4 | 4

5 | 6 8

6 | 5 7 9

7 | 1 5 7 8 8 9

8 | 0 2 5 7 8 8 9

9 | 7

**13. **(TCO 6) Horse race time is found to be normally distributed with a mean value of 18 minutes and a standard deviation of 4 minutes. Horses whose race time is in the top 6% will not be eligible to participate in a second round. What is the lowers race time that makes a horse losses his eligibility to participate in a second round? (Points : 6)

**1. **(TCO 8) For the following statement, write the null hypothesis and the alternative hypothesis. Also label which one is the claim.

Company X claims that the average salary for an entry level employee is $35,000 (Points : 8)

**2. **(TCO 11) A pizza restaurant manager claims that the average home delivery time for their pizza is no more than 18 minutes. A random sample of 36 home delivery pizzas was collected. The sample mean was found to be 19.25 minutes and the standard deviation was found to be 3.3 minutes. Is there evidence to reject the manager’s claim at alpha =.02? Perform an appropriate hypothesis test, showing the necessary calculations and/or explaining the process used to obtain the results. (Points : 20)

**4. **(TCO 6) The monthly utility bills are normally distributed with a mean value of $130 and a standard deviation of $15.

(a) Find the probability of having a utility bill between 100 and 150.

(b) Find the probability of having a utility bill less than $90.

(c) Find the probability of having a utility bill more than $160. (Points : 20)

**8. **(TCO 2) The ages of 10 students are listed in years:{ 17,20,18,24,21,26,29,18,22,28}

(a) Find the mean, median, mode, sample variance, and range.

(b) Do you think that this sample might have come from a normal population? Why or why not? (Points : 20)