Above what height are the tallest 2.5% of the…

Above what height are the tallest 2.5% of the city's girls?

Question 46

HardOriginal question

The heights of 15-year-old girls in a city are normally distributed with mean 150 cm and standard deviation 10 cm. (Take $P(0 < Z < 0.5) = 0.1915$ , $P(0 < Z < 1) = 0.3413$ , $P(0 < Z < 1.5) = 0.4332$ and $P(0 < Z < 1.96) = 0.4750$ .)

Above what height are the tallest 2.5% of the city's girls?

130.4 cmCorrect answerYour answer165 cmCorrect answerYour answer169.6 cmCorrect answerYour answer170 cmCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

The top 2.5% lie above $z = 1.96$ , since $0.5 - 0.4750 = 0.025$ .
$x = 150 + 1.96 \times 10 = 169.6$ cm.

Worth noting

130.4 cm marks off the shortest 2.5%.

Concept: A value from a share
Typical timeTypical: 150 s
Your timeYours: —

The rule this testsAreas under the curve

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Ten questions from Normal Distribution, at your own pace.

Practise this chapter →

Ten questions from Normal Distribution, at your own pace.

Above what height are the tallest 2.5% of the city's girls?

Question 46

Explanation