Question

Hey, could someone explain how to do this question? I know how to find z score but how do you find an x value when you're given z score?

Suppose X ~ N(9, 5). What value of x has a z-score of –0.5?

Answer 1

To find the value of x when given a z-score, you can use the formula z = (x - μ) / σ, where z is the z-score, x is the value of x, μ is the mean, and σ is the standard deviation. In this case, the value of x that has a z-score of -0.5 is 6.5.

Step-by-step explanation:

To find the value of x when given a z-score, you can use the formula z = (x - μ) / σ, where z is the z-score, x is the value of x, μ is the mean, and σ is the standard deviation. In this case, you are given a z-score of -0.5 and the normal distribution X ~ N(9, 5). Substitute the values into the formula:

-0.5 = (x - 9) / 5

Now, solve for x:

x - 9 = -0.5 * 5

x - 9 = -2.5

x = -2.5 + 9

x = 6.5

Therefore, the value of x that has a z-score of -0.5 is 6.5.