# Normal Probability Problems

Problem Set 2: Chapter 5, problems 6a, 6b, 24, 26;

6. For a population with a mean of µ =100 and standard deviation of ? = 10,

a. Find the z-score for each of the following X values.

X = 105 X = 120 X = 130

X = 90 X= 85 X = 60

b. Find the score (X value) that corresponds to each of the following z-scores.

z = -1.00 z = -0.05 z = 2.00

z = 0.70 z = 1.50 z = -1.50

24. Which of the following exam scores should lead to the better grade?

a. A score X =55 on an exam with µ =60 and ? = 5

b. A score of X = 40 on an exam with µ =50 and ? = 20

Explain your answer

26. A distribution with a mean of µ =38 and standard deviation ? = 20 is being transformed into a standardized distribution with µ =50 and ? = 10. Find the new, standardized score for each of the following values from the original population.

a. X = 48 b. X = 40

c. X = 30 d. X= 18

Chapter 6, problems 2, 4, 10, 12, 18

A kindergarten class consists of 14 days boys and 11 girls. If the teacher selects children from the class using random sampling,

a. What is the probability that the first child selected will be a girl?

b. If the teacher selects a random sample of n = 3 children and the first two children are both boys, what is the probability that the third child selected will be a girl?

What is sampling with replacement, and why is it used?

For a normal distribution, identify the z-scores location that would separate the distribution into two sections so that there is

a. 70% in the body on the right hand side.

b. 80% in the body on the right hand side.

c. 75% in the body on the left hand side.

d. 90% in the body on the left hand side.

#### Solution Summary

The solution provides step by step method for the calculation of X value and probability using the Z score. Formula for the calculation and Interpretations of the results are also included.