Question

The weights of boxes of candies produced in a factory are normally distributed with a mean weight of 16 oz and a standard deviation of 1 oz. What is the weight of a box of candies with a z-score of 2?

16 oz

18 oz

20 oz

22 oz

Answer 1

The weight of a box of candies is 18 oz

Option 2 is correct.

Explanation:

Given: The weights of boxes of candies produced in a factory are normally distributed with a mean weight of 16 oz and a standard deviation of 1 oz.

Formula:
`z=(x-m)/(\sigma)`

Mean: m = 16 oz

z-score: z = 2

Standard Deviation:
`\sigma = 1 oz`

Substitute the value into formula.

`2=(x-16)/(1)`

`2=x-16`

`x=18`

Hence, The weight of a box of candies is 18 oz

Answer 2

Let the required weight be X, then
z = (X - mean)/standard deviation
2 = (X - 16)/1
X - 16 = 2
X = 2 + 16
X = 18 oz.