Answer to Question #88979 in Statistics and Probability for Amelia

Question

Determine the z-score value in each of the following scenarios:
a. What z-score value separates the top 8% of a normal distribution from the bottom
92%?
b. What z-score value separates the top 72% of a normal distribution from the bottom
28%?
c. What z-score value form the boundaries for the middle 58% of a normal
distribution?
d. What z-score value separates the middle 45% from the rest of the distribution?
[12 marks]

Answer 1

a. P(Z<z)=0.92 -> z=1.4051.

b. P(Z<z)=0.28 -> z=-0.5828.

c. P(-z<Z<z)=0.58 -> P(Z<z)=0.5+0.58/2=0.79 -> z=0.8064.

So, the interval: (-0.8064, 0.8064).

d. P(-z<Z<z)=0.45 -> P(Z<z)=0.5+0.45/2=0.725 -> z=0.5978.

So, the interval: (-0.5978, 0.5978).