A confidence interval for a population mean is to be given at the $98\%$ level, using a normal distribution. State the value of $z$ used, to 3 decimal places.

Model answer

2.326

Also accepted: 2.3263, 2.33

Explanation

98\%

interval leaves

2\%

outside it, split as

1\%

in each tail, so

z

is the value with

0.99

of the distribution below it:

z = 2.326

. The commonly memorised

1.96

belongs to a

95\%

interval and

2.576

to a

99\%

interval.

Derived from ZIMSEC Additional Mathematics Paper 2, Specimen Paper, Q8

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