What percentage of the sugar packets weigh…

What percentage of the sugar packets weigh between 495 g and 505 g?

Question 50

EasyOriginal 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 $P(0 < Z < 2.5) = 0.4938$ .)

What percentage of the sugar packets weigh between 495 g and 505 g?

34.13%Correct answerYour answer68.26%Correct answerYour answer69.26%Correct answerYour answer95.44%Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

495 g and 505 g are $z = -1$ and $z = 1$ .
$2 \times 0.3413 = 0.6826$ , so 68.26%.

Worth noting

34.13% is only one side of the mean.

Concept: Within one standard deviation
Typical timeTypical: 90 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.

What percentage of the sugar packets weigh between 495 g and 505 g?

Question 50

Explanation