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%

Step-by-step 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 : $\sigma=\sqrt{\text{Variance}}=\sqrt{4}=2$

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

Z-score : $\dfrac{x-\mu}{\sigma}$

$z=\dfrac{15-10}{2}=2.5$

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%.