Question

Kori is analyzing a normal data distribution, but the data provided is incomplete. Kori knows that the mean of the data is 120 and that 84% of the data values are less than 130. Find the standard deviation for this data set.

Answer 1

Answer: for a more direct answer 10.1

i got this right on a test

Answer 2

SD = 10.1

Explanation:

We have been given that Kori knows that the mean of the data is 120 and that 84% of the data values are less than 130.

We will use z-score formula to find standard deviation of our given data set.

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

`z` = z-score,

`x` = Random sample score,

`\mu` = Mean,

`\sigma` = Standard deviation.

Let us find z-score corresponding to the area of population under curve less than 84%.

From normal distribution table we get that z-score corresponding to area less than 84% is 0.99.

Upon substituting our given values in z-score formula we will get,

`0.99=(130-120)/(\sigma)`

`0.99=(10)/(\sigma)`

`\sigma=(10)/(0.99)`

`\sigma=10.101010\approx 10.1`

Therefore, the standard deviation of our given data set is 10.1.