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

The expected value and standard deviation of the total number of silver wrappers=32,4.29

Step-by-step explanation:

Step 1

Let X represent holiday 1 binomial and Y represent holiday 2.

X + Y represent the total

Step 2

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

Step 3

Mean of a binomial distribution is calculated to be n * p

Step 4

Since both holidays are independent, the variance of the total is just the sum of the variances

Step 5

Variance of a binomial distribution is calculated to be n * p * (1-p). Side note, variance for a binomial distribution is maximized when p = 0.5

Step 6

We calculate  standard deviation, by taking the square root of the variance

Step 7

The expected value and standard deviation of the total number of silver wrappers=32,4.29

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step-by-step explanation: