The machine is adjusted so that the standard…

The machine is adjusted so that the standard deviation falls to 4 g, with the same mean.

Question 67

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

The machine is adjusted so that the standard deviation falls to 4 g, with the same mean. What percentage of sugar packets now weigh less than 490 g?

0.62%Correct answerYour answer1.24%Correct answerYour answer2.28%Correct answerYour answer49.38%Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

$z = \frac{490 - 500}{4} = -2.5$ .
$0.5 - 0.4938 = 0.0062$ , so 0.62%.

Worth noting

2.28% keeps the old standard deviation of 5 g.

Concept: A smaller spread thins the tails
Typical timeTypical: 150 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.

The machine is adjusted so that the standard deviation falls to 4 g, with the same mean.

Question 67

Explanation