Purchase Solution

Normal Probability & Area under the Standard Normal Curve

Not what you're looking for?

Ask Custom Question

Included with each section or problem are reference examples and end of section exercises that can be used as a guide. Be sure to show your work in case partial credit is awarded. To receive full credit, work must be shown if applicable.

Section 5.1: Introduction to Normal Distribution and the Standard Normal Distribution
1. Use the Standard Normal Distribution table to find the indicated area under the standard normal curve.
(References: example 3 - 6 pages 244 - 247, end of section exercises 21 - 40 page 249)

a. Between z = 0 and z = 1.24

b. To the right of z = 1.09

c. Between z = -1.56 and z = -0.15

d. To the left of z = -1.93

Section 5.2: Normal Distributions: Find Probabilities
(References: example 1 and 2 page 253, end of section exercises 13 - 30 pages 257 - 259

2. The diameters of a wooden dowel produced by a new machine are normally distributed with a mean of 0.55 inches and a standard deviation of 0.01 inches. What percent of the dowels will have a diameter less than 0.57?

3. The a loan officer rates applicants for credit. Ratings are normally distributed. The mean is 240 and the standard deviation is 50. Find the probability that an applicant will have a rating less than 260.

Section 5.3: Normal Distributions: Finding Values

4. Answer the questions about the specified normal distribution. (References: example 4 and 5 page 264 - 265, end of section exercises 39 - 45 pages 267 - 268)

a. The lifetime of ZZZ batteries are normally distributed with a mean of 280 hours and a standard deviation  of 10 hours. Find the number of hours that represent the 25th percentile.

b. Scores on an English placement test are normally distributed with a mean of 50 and standard deviation  of 2.5. Find the score that marks the top 10%.

Section 5.4: Sampling Distribution and the Central Limit Theorem

5. Find the probabilities.
(References: example 5 and 6 page 276 - 277, end of section exercises 25 - 31 pages 280 - 281)

a. From National Weather Service records, the annual snowfall in the TopKick Mountains has a mean of 72 inches and a standard deviation  of 12 inches. If the snowfall from 25 randomly selected years are chosen, what it the probability that the snowfall would be greater than 75 inches?

b. The loan officer rates applicants for credit. Ratings are normally distributed. The mean is 240 and the standard deviation is 60. If 36 applicants are randomly chosen, what is the probability that they will have a rating less than 260?

Attachments
Purchase this Solution
Solution Summary

The solution provides step by step method for the calculation of probability using the Z score and area under the standard normal curve. Formula for the calculation and Interpretations of the results are also included.

Purchase this Solution
Free BrainMass Quizzes
Measures of Central Tendency

Tests knowledge of the three main measures of central tendency, including some simple calculation questions.

Terms and Definitions for Statistics

This quiz covers basic terms and definitions of statistics.

Know Your Statistical Concepts

Each question is a choice-summary multiple choice question that presents you with a statistical concept and then 4 numbered statements. You must decide which (if any) of the numbered statements is/are true as they relate to the statistical concept.

Measures of Central Tendency

This quiz evaluates the students understanding of the measures of central tendency seen in statistics. This quiz is specifically designed to incorporate the measures of central tendency as they relate to psychological research.

View More Free Quizzes
Related BrainMass Solutions

  • Z-score and Area under the Normal curve

    266260 Z-Score and Area Under the Normal Curve Discuss the difference between a z-score and the area under the normal curve. What exactly does a z-score represent? What does the area under the graph of a normal probability distribution represent?

  • Probabilities using the Normal Distribution

    What is the area under a standard normal curve between z = −1.47 and z = 1.58? 0.8722 4. What is the area under a standard normal curve to the right of z = 0.35? 0.3632 5.

  • Statistics - Normal Distributions

    188956 Area under standard normal curve - Part 1) Sketch area under standard normal curve over the indicated intervals, and find the specified area. ...

  • Normal Probability and Z-score

    Convert 445 blood samples into a z-value (standard score). What is the area under the normal curve between 400 and 482? What is the area under the normal curve for ratings greater than 482? Interpret the result.

  • Standard Normal Distribution

    458786 Standard Normal Distribution Question 1 Use Appendix Table for Normal Distribution to find area under Standard Normal Distribution curve to the left of z = 0.85 Answer 0.8023 0.6245 0.3524

  • Normal distribution

    28329 Normal distribution 6.12 a. The area under the standard normal curve with parameters m = 64.4 and o= 2.4 that lies to the left of 61 is 0.0783.

  • Fresh Fruit Consumption - Normal Distribution

    (105 - 99.9)/4.87 = 1.05 P(98 < x < 105) = Area under the Standard Normal Curve between z1 = -0.39 and z2 = 1.05, which is 0.504 (c) z = (112 - 99.9)/4.87 = 2.48 P(x < 112) = Area under the Standard Normal Curve to the left of z = 2.48, which is

  • Normal Distribution, Standard Normal Distribution, Probability

    What is the difference between z scores and area in a bell curve? 3. T / F The number associated with the area under the bell curve that falls to the left of the mean or center line is a negative value (read this carefully).

  • Cable Companies - Normal Distribution

    z1 = (155 - 180)/8.48 = -2.95 and z2 = (170 - 180)/8.48 = -1.18 P(155 < x < 170) = Area under the Standard Normal Curve between z1 = -2.95 and z2 = -1.18, which is 0.118 (b) z = (200 - 180)/8.48 = 2.358 P(x < 200) = Area under the Standard Normal

  • Standard Normal Probability

    361214 Standard Normal Probability Determining the Z and X values when an area under the normal distribution curve is known. Find the value of z so that the are under the standard normal curve from 0 to z is .4772 and z is positive.

View More Related Solutions