# Statistics for business week 5

Individual Assignment

Unit:

Due Date:

Total Marks: STA101 – Statistics for Business Week 5

This assignment is worth 40% of the total marks in the unit.

Instructions:

1.Students are required to cover all stated requirements.

2.Your answer must be both uploaded to Moodle in word file and handed over a printed copy.

3.You need to support your answers with appropriate Harvard style references where necessary.

4.Include a title/cover page containing the subject title and code and the name, student idnumbers.

5.Please save the document as STA101AT1_first name_Surename_Student NumberEg: STA101AT1_John_Smith_NA20150000 1

a) P(A) (1 mark)

b) P(B)

c) P(A and B)

d) P(A or B)

e) P(A/B)

f) P(B/A)

(2 mark)

(2 mark)

(2 mark)

(2 mark)

(2 mark)

Question 1: (5 marks)

A basketball player has the following points for seven games: 20, 25, 32, 18, 19, 22, and 30.

Compute the following measures:

a) Compute the sample mean (the average of the points of each game) (1 mark)

b) Compute the sample median (2 mark)

c) Compute the variance and the standard deviation (2 marks)

Question 2: (5 marks)

Suppose during weekends, 55 percent of adults go to the beach, 45 percent go to the cinema,

and 10 percent go to both the beach and the cinema.

a) What is the probability that a randomly chosen adult does not go to the cinema? (1 marks)

b) What is the probability that a randomly chosen adult go to the beach or the cinema or

both? (2 marks)

c) What is the probability that a randomly chosen adult doesn’t go to the beach or the

cinema? (2 marks)

Question 3: (10 marks)

A Financial Consultant has classified his clients according to their gender and the

composition of their investment portfolio (primarily bonds, primarily stocks, or a balanced

mix of bonds and stocks). The proportions of clients falling into the various categories are

shown in the following table:

Portfolio Composition

Gender Bonds Stocks Balanced

Male 0.18 0.20 0.25

Female 0.12 0.10 0.15

One client is selected at random, and two events A and B are defined as follows:

A: The client selected is male.

B: The client selected has a balanced portfolio.

Find the following probabilities:

2

Question 4: (5 marks) Find the following probabilities by checking the z table

a)P(-1.52 < Z < 0.7)

b)P((1.15 < Z < 2.45)

c)P(-0.9 < Z < -0.3)

Question 5: (4 marks)

The foreman of a bottling plant has observed that the amount of soda in each “32-ounce” bottle is actually a normally distributed random variable, with a mean of 32.2 ounces and a standard deviation of 0.3 ounce.

a)If a customer buys one bottle, what is the probability that the bottle will contain more than32 ounces? (2 marks)

b)If a customer buys a carton of four bottles, what is the probability that the mean amount ofthe four bottles will be greater than 32 ounces? (2 marks)

3

Question 6: (10 marks)

a, What are the common types data? Gives the defination of them and example?

b, Explain what is Coefficient of Correlation? Give examples of each form and draw with

a graph?

4

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