98.2k views
1 vote
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

User Norrisa
by
8.3k points

2 Answers

5 votes

Answer:

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.

7 votes

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.

User Saif Asif
by
7.9k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories