Question

The lengths of spools of ribbon are normally distributed with a mean of 91.4 centimeters and a standard deviation of 1.3 centimeters.

What is the length of a spool of ribbon with a z-score of 0.7?



Enter your answer, rounded to the nearest tenth, in the box.

Answer 1

the length of a spool of ribbon with a z-score of 0.7 is 92.3 cm

Explanation:

Here we have , The lengths of spools of ribbon are normally distributed with a mean of 91.4 centimeters and a standard deviation of 1.3 centimeters. What is the length of a spool of ribbon with a z-score of 0.7 . Let's find out:

According to Question we have following parameters as :

X = the length of a spool of ribbon

Mean(x) = 91.4 cm

standard deviation(y) = 1.3 cm

Z = 0.7

We know that Z score is given by :

⇒
`Z = (X-Mean)/(\Standrad deviation)`

⇒
`0.7 = (X-91.4)/(1.3)`

⇒
`0.91 = X-91.4`

⇒
`X=92.3cm`

Therefore , the length of a spool of ribbon with a z-score of 0.7 is 92.3 cm