Question

For a normal distribution with a mean (μ) of 85.1 and a standard deviation (σ) of 4.82, use the formula z = (x - μ) / σ. Plug in the values and solve for x:

Find the data value corresponding to the value of z given (provide the answer rounded to four decimal places).

Answer 1

The data value corresponding to the given value of z is approximately 89.678 when rounded to four decimal places.

Step-by-step explanation:

The formula given is z = (x - μ) / σ. We are asked to find the data value (x) corresponding to a given value of z. In this case, we are given the mean (μ) as 85.1 and the standard deviation (σ) as 4.82. We need to solve the equation for x using the given values:

z = (x - 85.1) / 4.82

Multiplying both sides of the equation by 4.82 gives:

4.82z = x - 85.1

Adding 85.1 to both sides of the equation gives:

x = 4.82z + 85.1

Now we can substitute the value of z you have and solve for x:

x = 4.82(0.9) + 85.1 = 89.678

Therefore, the data value corresponding to the given value of z is approximately 89.678 when rounded to four decimal places.