Question

Hello

Could you kindly verify if my answers are correct:

Question 1)

A distribution has a standard deviation of 10. Find the z-score for each of the following
locations in the distribution.
a. Above the mean by 5 points
b. Above the mean by 2 points
c. Below the mean by 20 points
d. Below the mean by 15 point

My answers are:

a) +0.50

b) + 0.20

c) -2.00

d) -1.50

Question 2:

Subjective wellbeing was measured among a sample of final year law students, with M = 150
and s2 = 25. Determine the z scores for the students who obtained the following scores on
the subjective wellbeing measure:

a. 100
b. 120
c. 140
d. 160

My answers are:

a) -10

b) -6

c) -2

d) +2

Question 3

For a population with ? = 48 and ? = 8, find the X value that corresponds to each of the
following z-scores:
a. – 0.25
b. – 1.50
c. 0.50
d. 2.00

My answers are:

a) 46

b) 36

c)52

d)64

Question 4

A normal distribution has ? = 80 and ? = 10. What is the probability of randomly selecting
the following scores:
a. X > 75
b. X > 85
c. X < 90
d. X < 60

My answers are:

a) .3085

b) .6915

c) .8413

d) .0228

Question 5

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?

My answers are:

a) +1.41

b) -0.58

c) -0.81 and +0.81

d) -0.60 and +0.60

Question 6

Assume that the total score (from both teams) for college football games averages ? = 42
points per game, and that the distribution of total points is approximately normal with ? =
20.
a. What is the probability that a randomly selected game would have more than 60
points?
b. What proportion of college football games have a point total between 20 and 60?

My answers are:

a) .8159

b) .1357

Question 7

Each of the following samples was obtained from a population with ? = 100 and ? = 10. Find
the z-score corresponding to each sample mean.
a. M = 95 for a sample of n = 4
b. M = 104 for a sample of n = 25
c. M = 103 for a sample of n = 100

My answers are:

a) .1587

b) .9772

c) .9987

Answer 1

Given, distribution has a standard deviation of 10 a) above the mean by 5 points x - mu = 5 z-score z = x - mu/sigma = 5/10 = 0.5 above the mean by 2 points x - mu = 2 z-score z = x - mu/sigma = 2/10 = 0.2 below the mean by 20 points x - mu = -20 z-score z = x - mu/sigma = -15/10 = -1.5 given mean m = 150 and variance s^2 = 25 s = 5 z-score at x - mu/sigma = -15/10 = -1.5 given mean m = 150 and variance s^2 = 25 s = 5 z-score at 100 z = x - m/s = 100 - 150/s = -10 z-score at 120 z = x - m/s = 120 - 150/5 = -6 z-score at 140 z = x - m/s = 140 - 150/5 = -2 z - score at 160 z = x - m/s = 160 - 150/5 = 2