Question 1

Paper 2, calculatorEasy4 marks

A psychologist models scores on a test as a normally distributed random variable XX measured in points. Figure 1 shows two cumulative probabilities for this distribution.

20304050607080x (score, points)fX(x)P(X≤42)=0.20P(X≤58)=0.854258
(a)

Using a GDC, determine the zz-value corresponding to X=42X=42 Give your answer to four significant figures.

[1]
(b)

Using a GDC, determine the zz-value corresponding to X=58X=58 Hence use both zz-values to determine the mean and standard deviation of XX giving each answer to three significant figures.

[3]

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