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
Explain the following concepts:
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 (University graduate)
Prob (A University graduate)
Prob (University graduate A)
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)
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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