Reference no: EM131539917

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?