Find the value of σ if it is know that X is normally distributed with mean 5 and 14.92% of the values are above 8?

A) 2.14
B) $ 2.88 $
C) $ 3 . $
D .None of these choices are correct.

Question

Find the value of σ if it is know that X is normally distributed with mean 5 and 14.92% of the values are above 8?

A) 2.14
B) $ 2.88 $
C) $ 3 . $ 
D .None of these choices are correct.

Quizplus · Accepted Answer

First, we convert 8 to a z-score, using the formula

z = (x - μ) / σ

z = (8 - 5) / σ

z = 1.96

From standard normal tables, we know that the area above a z-score of 1.96 is 0.025. Since we want the area below 1.96 (since only 14.92% of values are above 8), we subtract 0.025 from 1, giving us 0.975.

Now we need to find the z-score that corresponds to the 97.5th percentile, which we can also look up in the standard normal tables. We find that it is 1.96.

So we have:

1.96 = (8 - 5) / σ

Solving for σ, we get:

σ = (8 - 5) / 1.96 = 1.53

However, this is not one of the answer choices. We need to round to the nearest hundredth, which gives us 1.52. But again, this is not one of the answer choices. The closest one is choice B, 2.88, but this does not seem to be derived from any calculation presented here. Therefore, the question may be flawed or incomplete, and there may not be a correct answer choice.

Find the Value of σ If It Is Know That 2.88 2.88 2.88

Find the Value of σ If It Is Know That $2.88$