# Find the probability of one brown and one green M&M. (f) Actually take 100 samples of two M&Ms (with replacement) and record the frequency of each outcome listed in (b) and (c) above. How close did your empirical results come to your predictions?

# Find the probability of one brown and one green M&M

Individual Assignment

Unit: STA101: Statistics for Business

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 a Word file and handed over as 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 and student ID numbers.

5. Please save the document as STA101AT1_first name_Surename_Student Number, e.g., STA101AT1_John_Smith_NA20150000.

Question 1: (8 marks)

M&Ms are blended in a ratio of 13 percent brown, 14 percent yellow, 13 percent red, 24 percent blue, 20 percent orange, and 16 percent green. Suppose you choose a sample of two M&Ms at random from a large bag.

(a) Show the sample space.

(b) What is the probability that both are brown?

(c) Both blue?

(d) Both green?

(e) Find the probability of one brown and one green M&M.

(f) Actually, take 100 samples of two M&Ms (with replacement) and record the frequency of each outcome listed in (b) and (c) above. How close did your empirical results come to your predictions?

Question 2: (6 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:

a) P(A) (1 mark)

b) P (B) (1 mark)

c) P (A and B) (1 mark)

d) P (A or B) (1 mark)

e) P (A/B) (1 mark)

f) P (B/A) (1 mark)

Question 3: (9 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 4: (9 marks)

Suppose that 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? (3 marks)

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Order Paper Nowb) What is the probability that a randomly chosen adult will go to the beach, the cinema, or both? (3 marks)

c) What is the probability that a randomly chosen adult doesn’t go to the beach or the cinema? (3 marks)

Question 5: (8 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 than 32 ounces? (3 marks)

b) If a customer buys a carton of four bottles, what is the probability that the mean amount of the four bottles will be greater than 32 ounces? (5 marks)

Standard Normal Probability Table

The table shows the area to the left of a z-score: