Question

Carl's Candies has determined that a candy bar measuring 3 inches long has a z-score of +1 and a candy bar measuring 3.75 inches long has a z-score of +2.

What is the standard deviation of the length of candy bars produced at Carl's Candies?


A 0.75

B 3

C 3.75

D 2

Answer 1

A. d = 0.75.

Explanation:

The z-score =( x - m) / d where m = the mean and d = the standard deviation.

So we have

(3 - m) / d = 1

3 - m = d.............(1)

and

(3.75 - m) / d = 2

3.75 - m = 2d....... (2)

Subtract (2) - (1):

0.75 = d.

Answer 2

Answer: A 0.75

Explanation:

Formula for z-score :

`z=(x-\mu)/(\sigma)`

, where x= random variable

`\mu` = Population mean

`\sigma` = Standard deviation

As per given , we have

`+1=(3-\mu)/(\sigma)\\\\\Rightarrow\ \sigma=3-\mu\\\\\Rightarrow\ \mu=3-\sigma---(i)`

`+2=(3.75-\mu)/(\sigma)\\\\\Rightarrow\ \mu=3.75-2\sigma---(ii)`

From (i) and (ii) , we have

`3-\sigma=3.75-2\sigma\\\\\Rightarrow\ 2\sigma-\sigma=3.75-3\\\\\Rightarrow\ \sigma=0.75`

Hence, the standard deviation of the length of candy bars produced at Carl's Candies is 0.75.

Thus , the correct answer is A. 0.75.