Out of 20,000 sugar packets, about how many…

Out of 20,000 sugar packets, about how many weigh between 490 g and 510 g?

Question 59

MediumOriginal question

A machine fills packets of sugar. The weights are normally distributed with mean 500 g and standard deviation 5 g. (Take $P(0 < Z < 1) = 0.3413$ , $P(0 < Z < 2) = 0.4772$ and $P(0 < Z < 2.5) = 0.4938$ .)

Out of 20,000 sugar packets, about how many weigh between 490 g and 510 g?

912

Correct answerYour answer

9{,}544

Correct answerYour answer

13{,}652

Correct answerYour answer

19{,}088

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

490 g to 510 g is $z = -2$ to $z = 2$ : $2 \times 0.4772 = 0.9544$ .
$0.9544 \times 20{,}000 = 19{,}088$ packets.

Worth noting

912 is the number outside that range.

Concept: A count from a share
Typical timeTypical: 120 s
Your timeYours: —

The rule this testsUsing the normal distribution

Practise this chapter →

Ten questions from Normal Distribution, at your own pace.

Practise this chapter →

Ten questions from Normal Distribution, at your own pace.

Out of 20,000 sugar packets, about how many weigh between 490 g and 510 g?

Question 59

Explanation