Question

Suppose a variable X (systolic blood pressure) is normally distributed with a variance of 36. If approximately 0.25 of the values of X are less than 88, what is the mean of X g?

Answer 1

92.044

Explanation:

The variance = 36

σ² = 36 = 6

The probability that x is less than 88 is equal to 0.25

So probability of (x<z) = 0.25

From the z table, z = -0.674

Using the z formula,

z = x-u/σ

Z = -0.674

X = 88

σ = 6

When we insert these formula we have:

-0.674 = 88 - u/6

6 x -0.674 = 88- u

-4.044 = 88 - u

92.044 = u

Therefore from the calculations above the mean of X is 92.044 and it is approximately 92.