What is the z-score of a girl in the city who…

What is the z-score of a girl in the city who is 165 cm tall?

Question 31

EasyOriginal 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 $P(0 < Z < 1.96) = 0.4750$ .)

What is the $z$ -score of a girl in the city who is 165 cm tall?

-1.5

Correct answerYour answer

0.15

Correct answerYour answer

1.5

Correct answerYour answer

15

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

$z = \frac{x - \mu}{\sigma}$ .
$\frac{165 - 150}{10} = 1.5$ .

Worth noting

15 is the distance from the mean in cm, before dividing by the standard deviation.

Concept: The standard score
Typical timeTypical: 90 s
Your timeYours: —

The rule this testsAreas under the curve

Practise this chapter →

Ten questions from Normal Distribution, at your own pace.

Practise this chapter →

Ten questions from Normal Distribution, at your own pace.

What is the z-score of a girl in the city who is 165 cm tall?

Question 31

Explanation