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Chapter 10: Q. 7 (page 667)

A certain candy has different wrappers for various holidays. During Holiday 1the candy wrappers are 30%silver, 30%red, and 40%pink. During Holiday 2the wrappers are 50%silver and 50%blue. Forty pieces of candy are randomly selected from the Holiday 1distribution, and 40 pieces are randomly selected from the Holiday 2 distribution. What are the expected value and standard deviation of the total number of silver wrappers?

Short Answer

Expert verified

Result is:

32,4.29

Step by step solution

01

Given information

We have been give that

X~binomial(40,0.3)Y~binomial(40,0.5)

Each distributio follows a binomial distribution.

02

Simplify

For any distribution, if they are independent, the mean of the sum is just the sum of means.

Mean(X+Y)=Mean(X)+Mean(Y)

Mean of a binomial is calculated ton*p

Mean(X)=40*0.3=12,Mean(Y)=40*0.5=20

Since both holidays are independent

Var(X+Y)=Var(X)+Var(Y)

Variance for a binomial distributed is maximised

Var(X)=40*0.3*(1-0.3)=8.4,Var(Y)=40*0.5*

0.5=10Var(X+Y)=18.4

We will calculate standard deviation by

SD(X+Y)=Var(X+Y)=4.29

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