Statistics: understanding z-scores and probabilities of obse

I would like some help with the following problems. Can I please get the actual manual work for the problems so I can follow the formula and follow the steps with other word problems. Thanks.

1. A normal population has a mean of 20.0 and a standard deviation of 4.0.
a. compute the z value associated with 25.0.
b. what proportion of the population is between 20.0 and 25.0?
c. what proportion of the population is less than 18.0?

2. The amounts of money requested on home loan applications at Down River Federal Savings follow the normal distribution, with a mean of $70,000 and a standard deviation of $20,000. A loan application is received this morning.
What is the probability.
a. the amount requested is $80,000 or more?
b. the amount requested is between $65,000 and $80,000?
c. the amount requested is $65,000 or more?

3. A study found that a mean waiting time to see a physician at an outpatient clinic was 40 minutes with a standard deviation of 28 minutes. a. what is the probability of more than an hours wait.
b. less than 20 minutes.
c. at least 10 minutes.

4. the credit score of a 35 yr old applying for a mortgage at Ulysses Mortgage Associates is normally distributed with a mean of 600 and a standard deviation of 100.
a. find the credit score that defines the upper 5 percent.
b. seventy-five percent of the customers will have a credit score higher than what value?
c. within what range would the middle 80 percent of credit scores lie.

Solution Summary

A step by step solution to all the problems is provided. It shows how to find probabilities from a normal distribution.

A continuous random variable, x, is normally distributed with a mean of $1000 and a standard deviation of $100. Convert each of the following x values into its corresponding z-score.
a. x = $1000
b. x = $750
c. x = $1100
d. x = $950
e. x = $1225
2.Using the standard normal table, find the following probabilities

7.12
A random sample is obtained from a population with a mean of 50 and a standard deviation of 12.
A. For a sample of n = 4 scores, would a sample mean of M = 55 be considered an extreme value or is it a fairly typical sample mean?
B. For a sample mean of n = 36, would a sample mean of M = 55 be considered an extre

Binomial Probabilities
These procedures show how to get binomial probabilities associated with n = 5 trials when the probability of a success on any given trial is π = 0.20.
Procedure I: Individual or cumulative probabilities for x = 2 successes.
Procedure II: Complete set of individual

Examples
Fill in the answers for each table below. Please report your z scores to two decimals and your p values to three decimals. If the p value is less than .001, please report p < .001.
µ=25 σ=2
X z p(z)
33
35
43
22
17
µ=25 σ=5
X z p(z)
33
35
43
22
17
µ

Use the following contingency table:
Event A Event B
Event C 9 6
Event D 4 21
Event E 7 3
Determine the following probabilities:
a) P (A and C)
b) P (A and D)
c) P B and E)
d) P (A and B)

1. A sample of n = 7 scores has a mean of M = 5. After one new score is added to the sample the new mean is calculated to be M = 6. The new score was X = 13. (Points: 1)
True
False
2. What is the mean for the following sample of scores?
Scores: 1, 2, 5, 4 (Points: 1)
12
6
4

Assign decimal numbers for probabilities in table below for each x.
Don't forget: total for all probabilities should be exactly 1.
x = 0 1 2 3 4
-------------------------------------
P(x) =
Based on your probability table:
1. Find probability that x is less than 3, P (x < 3)
2. Find pro

6.3. Find the following probabilities for the standard normal random variable z: {see attachment}
6.7. Find a Zo that has area .9505 to its left.
Find a Zo that has area .05 to its left.