Question

If z-score of normal distribution is 2.5, mean of distribution is 45 and standard deviation of normal distribution is 3 then value of x for a normal distribution is

Answer 1

Answer:

z = (x - mean) / standard deviation

2.5 = (x - 45)/3

7.5 = x - 45

x = 45 + 7.5

x = 52.5

Answer 2

Answer:

The value of the X is given by 3000

Step-by-step explanation:

The invNorm function on your TI-84 calculator will calculate z score of a certain area (probability). A 2.5% (0.025) portion of the curve to the right equates to 1 - 0.025 or 0.975 to the left. So, if you do invNorm(0.975) it will give you the z score associated with a 97.5% area.

invNorm(0.975) = 1.959964

To turn that z-score into a standard deviation, use the equation for z-score.

z-score = (x - μ)/σ or σ =  (x - μ)/Z = (50.88 - 45)/1.959964 = 5.88/1.959964 = 3.000

So the standard deviation is 3.000