What percentage of the sugar packets weigh…

What percentage of the sugar packets weigh less than 490 g?

Question 49

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 less than 490 g?

2.28%Correct answerYour answer4.56%Correct answerYour answer47.72%Correct answerYour answer97.72%Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

$z = \frac{490 - 500}{5} = -2$ .
$0.5 - 0.4772 = 0.0228$ , so 2.28%.

Worth noting

4.56% counts both tails, light and heavy.

Concept: A lower tail
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 less than 490 g?

Question 49

Explanation