**Question 1**

David set a mathematics quiz for his students. The quiz is marked out of 10. His students’ marks are summarized in the table below:

Construct an appropriate frequency table and draw a histogram to depict the data above

Compute the mean

Calculate the variance and standard deviation

Calculate the coefficient of variation

Interpret the distribution of marks as shown in your histogram

**Question 2**

Explain the following concepts:

Confidence levels

Qualitative data

Multiplication rule

Bayes’ Law

**Question 3**

**Part 1**

A researcher collected a sample of 50 respondents in a shopping mall on a weekend. The data are organized in the table below:

Calculate the following probabilities

Prob (A)

Prob (University graduate)

Prob (A University graduate)

Prob (University graduate A)

**Part 2**

The random variable Y follows a normal distribution with mean µ and variance σ2 , i.e. Y N(µ, σ2). Suppose we have the following information:

P(X ≤ 66) = 0.0421 and P(X ≥ 81) = 0.1298

(a) Compute the value of σ = 5

(c) Calculate P(65 ≤ X ≤ 74)

**Question 4**

A sample of test scores is obtained. The scores are displayed as follows:

11, 16, 19, 15, 7, 8, 10

Test the hypothesis that the mean score is 15 at a 1% significance level

A chemical manufacturer is concerned about the degree of contamination in the raw material shipments purchased from a supplier. Taking a random sample of 20 shipments of raw materials, the standard deviation of contamination is 3.59. Construct the 95% confidence interval for population variance.

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