Assignment: Business Statistics
Question 1
The following shows the temperatures (high, low) and weather conditions in a given Sunday for some selected world cities. For the weather conditions, the following notations are used: c = clear; cl = cloudy; sh = showers; pc = partly cloudy.
City Hi Lo Condition
Acapulco 99 77 pc
Bangkok 92 78 pc
Mexico City 77 57 sh
Montreal 72 56 pc
Paris 77 58 c
Rome 88 68 cl
Toronto 78 61 c
1 How many elements are in this data set?
2 How many variables are in this data set?
3 How many observations are in this data set?
4 Name the variables and indicate whether they are categorical or quantitative.
Question 2
A student has completed 20 courses in the School of Arts and Sciences. Her grades in the 20 courses are shown below.
A B A B C
C C B B B
B A B B B
C B C B A
1 Develop a frequency distribution and a bar chart for her grades.
2 Develop a relative frequency distribution for her grades and construct a pie chart.
Question 3
The number of hours worked per week for a sample of ten students is shown below.
Student Hours
1 20
2 0
3 18
4 16
5 22
6 40
7 8
8 6
9 30
10 40
1 Determine the median and explain its meaning.
2 Compute the 70th percentile and explain its meaning.
3 What is the mode of the above data? What does it signify?
Question 4
You are given the following information on Events A, B, C, and D.
P(A)= .4 P(A U D) = .6
P(B)= .2
P(C)= .1 P(A | B) = .3
P(A ∩ C)= .04 P(A ∩ D)= .03
1 Compute P(D).
2 Compute P(A ∩ B).
3 Compute P(A | C).
4 Compute the probability of the complement of C.
5 Are A and B mutually exclusive? Explain your answer.
6 Are A and B independent? Explain your answer.
7 Are A and C mutually exclusive? Explain your answer.
8 Are A and C independent? Explain your answer.
Question 5
1 When a particular machine is functioning properly, 80% of the items produced are non-defective.
2 If three items are examined, what is the probability that one is defective?
3 Use the binomial probability function to answer this question.
Question 6
The average starting salary of this year's graduates of a large university (LU) is $20,000 with a standard deviation of $8,000. Furthermore, it is known that the starting salaries are normally distributed.
1 What is the probability that a randomly selected LU graduate will have a starting salary of at least $30,400?
2 Individuals with starting salaries of less than $15,600 receive a low income tax break. What percentage of the graduates will receive the tax break?
3 What are the minimum and the maximum starting salaries of the middle 95.4% of the LU graduates?
Question 7
A simple random sample of 6 computer programmers in Houston, Texas revealed the sex of the programmers and the following information about their weekly incomes.
Programmer Weekly Income Sex
A $250 M
B 270 M
C 285 F
D 240 M
E 255 M
F 290 F
1 What is the point estimate for the average weekly income of all the computer programmers in Houston?
2 What is the point estimate for the standard deviation of the population?
3 Determine a point estimate for the proportion of all programmers in Houston who are female.
Question 8
Students of a large university spend an average of $5 a day on lunch. The standard deviation of the expenditure is $3. A simple random sample of 36 students is taken.
1 What are the expected value, standard deviation, and shape of the sampling distribution of the sample mean?
2 What is the probability that the sample mean will be at least $4?
3 What is the probability that the sample mean will be at least $5.90?