Question

The number of calories in peanut M&Ms have an approximately normal distribution with mean 10 calories per M&M and variance 4. What percentage of peanut M&Ms are more than 15 calories

Answer 1

Answer: 0.62%

Explanation:

Given : The number of calories in peanut M&Ms have an approximately normal distribution with

`\mu=10\text{ calories per }M\&M`

Standard deviation :
`\sigma=\sqrt{\text{Variance}}=√(4)=2`

Let x be the amount of calories in a randomly selected peanut M&Ms.

Z-score :
`(x-\mu)/(\sigma)`

`z=(15-10)/(2)=2.5`

The probability that the peanut M&Ms are more than 15 calories using standardized normal distribution table :

`P(x>15)=P(z>2.5)=1-P(z<2.5)\\\\=1-0.9937903=0.0062097`

In percent ,
`0.62097\%\approx0.62\%`

Hence, the percentage of peanut M&Ms are more than 15 calories is 0.62%.