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Chapter 12: Q. 8 (page 800)

A large machine is filled with thousands of small

pieces of candy, 40%of which are orange. When money

is deposited, the machine dispenses 60randomly selected

pieces of candy. The machine will be recalibrated if a

group of 60candies contains fewer than18 that are

orange. What is the approximate probability that this will

happen?

a)Pz<0.3-0.4(0.4)(0.6)60

b)Pz<0.4-0.3(0.3)(0.7)60

role="math" localid="1650519113387" c)Pz<0.3-0.4(0.4)(0.6)60

role="math" localid="1650519757907" d)Pz<0.3-0.4(0.4)(0.6)60

e)Pz<0.4-0.3(0.3)(0.7)60

Short Answer

Expert verified

The answer is optiona)Pz<0.3-0.4(0.4)(0.6)60

Step by step solution

01

Given Information

40%of the small candies are orange.

On depositing money, the machine dispenses 60randomly selected pieces of candy.

The machine will be recalibrated if a group of 60candies contains fewer than 18that are orange.

02

Simplification

The problem is about population proportions. The problem states that 40%are orange indicating the true population proportion being 0.4.

The Z score formula for proportions is:

Z=p^-pp脳(1-p)n

18of the 60candies is 30percent. Therefore, the correct boundary when plugging in the number is:

Z=0.3-0.40.4脳0.660

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