Question

The number of potato chips in a bag is normally distributed with a mean of 75 and a standard deviation of 5. Approximately what percent of bags contain between 65 and 85 potato chips?
Approximately 68%
Approximately 75%
Approximately 95%
Approximately 99.7%

Answer 1

Approximately 95% of bags contain between 65 and 85 potato chips.

Step-by-step explanation:

step 1 :

Given,

The mean, M = 75

Standard deviation, SD = 5

step 2 :

From Normal distribution,

The left side of mean is 32% = M-SD, 16% = M-2SD and 2% = M-3SD

The right side of mean is 32% = M+SD, 16% = M+2SD and 2% = M+3SD

step 3 :

Calculate for left side: M-SD = 75-5 = 70 and M-2SD = 75-10 = 65

Calculate for right side: M+SD = 75+5 = 80 and M+2SD = 75+10 = 85

step 4 :

Calculate the percentage between 65 and 85:

(M-SD) + (M-2SD) + (M+SD) + (M+2SD) = 32% + 16% + 32% + 16%

                                                               = 96 % (which is approximately 95 %)