Statistics assignment

Mid-Term Exam

1. The following data set shows the number of hours of sick leave that some of the

employees of Bastien’s, Inc. have taken during the first quarter of the year.(20 points)

19 22 27 24 28 12

23 47 11 55 25 42

36 25 34 16 45 49

12 20 28 29 21 10

59 39 48 32 40 31

a. Develop a frequency distribution for the above data (Let the width of your class be 10

units and start your first class as 10-19)

b. Develop a relative frequency distribution and percent frequency distribution for the

data

c. Develop a cumulative frequency distribution

d. How many employers have taken less than 40 hours of sick leave?

2. A researcher has obtained the number of hours worked per week during the summer for a

sample of fifteen students. Please make sure you must use the manual procedure

explained in your textbook in chapter 3. You should also show mathematical steps

in detail. Your answer will be marked down by 50% if you just include the final

answer.(20 points)

40 25 35 30 20 40 30 20 40 10 30 20 10 5 20

a. Calculate mean, range, and standard deviation.

b. Calculate 40 th

percentile and median.

3. Assume you have applied for two jobs A and B. The probability that you get an offer for

job A is 0.23. The probability of being offered job B is 0.19. The probability of getting at

least one of the jobs is 0.38. You should also show mathematical steps in detail. Your

answer will be marked down by 50% if you just include the final answer. (20 points)

a. What is the probability that you will be offered both jobs?

b. Are events A and B mutually exclusive? Why or why not? Explain.

4. The average starting salary of this year’s graduates of a large university (LU) is $10,000

with a standard deviation of $5,000. Furthermore, it is known the starting salaries are

normally distributed. You should also show mathematical steps in detail. Your

answer will be marked down by 50% if you just include the final answer. (30 points)

a. What is the probability that a randomly selected LU graduate will have a starting

salary of at least $20,500?

b. The sample size for a large university (LU) is 150,000 this year, and individuals with

starting salaries of less than $15,600 receive a low income tax break. How many of

the LU graduates will receive a low income tax break?