Question

I keep getting 70 but that's not an answer??

Betty's bite size candies are packaged in bags the number of candies per bag is normally distributed with a mean of 50 candies and a standard deviation of 3. At a quality control checkpoint a sample of bags is checked and 12 bags contain fewer than 47 candies how many bags were probably taken as samples?

a) 15
b) 75
c) 36
d) 24

Answer 1

The standard deviation is 3 , so 50 -47 = 3, means the 47 candies is 1 deviation below the mean.

A normal distribution, 68% of the sample falls within 1 standard deviation, which means 100-68 = 32 is out side the mean. Half of that, 32 / 2 = 16% is above and the other half (16%) would be below.

12 bags were below, so we would do a ratio, with the percentages as a whole number, so 16% = 16 and 100% = 100:

12/16 = X/100

Cross multiply: 16x = 1200

Divide both sides by 16:
X = 1200/16
X = 75


The answer is 75 bags were tested.