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- A mixture of short answer and multiple-choice questions
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- Question 1 of 10
##### 1. Question

Estimate the mean of the data.

\( \begin{array}{|c|c|c|c|c|c|} \hline

Class & 0 \le x < 50 & 50 \le x < 100 & 100 \le x < 150 & 150 \le x < 200 & 200 \le x < 250 \\ \hline Frequency (f) & 3 & 9 & 16 & 18 & 17 \\ \hline \end{array} \)Sum of scores \( = \) \( \times 3 + \) \( \times 9 + \) \( \times 16 + \) \( \times 18 + \) \( \times 17 = \)

Sum of frequencies \( = \) \( + \) \( + \) \( + \) \( + \) \( = \)

Mean \( = \) \( \div \) \( = \) , correcting to one decimal place

CorrectIncorrect - Question 2 of 10
##### 2. Question

Select the corresponding frequency table for the cumulative frequency graph shown.

CorrectIncorrect - Question 3 of 10
##### 3. Question

Find \( a, b, c \) and the mean.

\( \begin{array}{|c|c|c|} \hline

Score (x) & Frequency (f) & f \times x \\ \hline

100 & 1 & 100 \\ \hline

200 & 6 & 1200 \\ \hline

300 & a & 2700 \\ \hline

400 & 7 & 2800 \\ \hline

500 & b & 1000 \\ \hline

Total & c & 7800 \\ \hline

\end{array} \)\(a = \)

\(b = \)

\(c = \)

\( \bar x = \)

CorrectIncorrect - Question 4 of 10
##### 4. Question

Find the interquartile range of the data represented in the box-and-whisker plot.

\( \begin{array}{c|cccccc}

1 & 0 & 1 &&&& \\

2 & 1 & 2 & 6 &&& \\

3 & 2 & 4 & 7 & 7 && \\

4 & 3 &&&&& \\

\end{array} \)List the scores in ascending order.

The upper quartile is .

The lower quartile is .

The interquartile range is .

CorrectIncorrect##### Hint

Interquartile Range = Upper Quartile – Lower Quartile

- Question 5 of 10
##### 5. Question

A box contains balls numbered \( 1 \) to \( 50 \). One ball is taken randomly out of the box. Find the probability that it is a multiple of \( 12 \), given that it is a multiple of \( 3 \). Answer to two decimal places.

CorrectIncorrect - Question 6 of 10
##### 6. Question

Find \(P\left( {X > 2} \right)\).

\( \begin{array} {|c|c|c|c|c|c|} \hline

x & 0 & 1 & 2 & 3 & 4 \\ \hline

P( X = x ) & 0.2 & 0.3 & 0.2 & 0.1 & 0.2 \\ \hline

\end{array} \)CorrectIncorrect - Question 7 of 10
##### 7. Question

Five per cent of items made by a factory machine are defective. The items are packed and sold in boxes of 20. Find the probability of at least one items being defective in a box, correcting to four decimal places.

CorrectIncorrect - Question 8 of 10
##### 8. Question

A binomial random variable has a mean of 10 and a variance of 5. Find \(\Pr \left( {X = 3} \right)\), correcting to four significant figures.

CorrectIncorrect - Question 9 of 10
##### 9. Question

Find the score if a \(z\)-score is 2.3 when the standard deviation is 5.1 and the mean is 55.

CorrectIncorrect - Question 10 of 10
##### 10. Question

In which of the following subjects did John achieve his best result?

\( \begin {array} {|c|c|c|} \hline

subject & mean & standard \ deviation & John’s \ mark \\ \hline

chemist & 75 & 7 & 73 \\ \hline

economy & 70 & 6 & 73 \\ \hline

finance & 65 & 5 & 73 \\ \hline

geography & 80 & 8 & 73 \\ \hline

\end{array} \)\(z\)-score on chemistry:

\(z\)-score on economy:

\(z\)-score on finance:

\(z\)-score on geography:

Which is the best result? (chemistry/economy/finance/geography)

CorrectIncorrect