MGT 5028 Week 4 Assignment -Application Questions and Problems

Week 4: Normal Distribution and probability theory
Introduction: Normal Curves,
Central Limit Theorem, and Probability
At the heart of many statistical
concepts is the idea of normality. Not normality as in a normal or typical
individual, but a normality of distribution of scores that includes scores that
are far from normal or average. Assumptions about the distributions of scores
and of the distribution of the averages of scores from samples are powerful
tools for making sense of the world. Also powerful is knowledge of the place of
chance in research findings, how statistics can be used to estimate if findings
are due to chance, and utilizing this information to help us make decisions.

The chapter readings for this assignment are critical as they include the
concepts of probability and normal distribution. In our daily lives, most
results are probabilistic and fail to have definitive and absolutes involved.
Review the resources listed in the
Books and Resources area below to prepare for this week’s assignments.

Books and Resources for week 4: Books and Resources for
this Week:

Books

Reference

Instruction

Statistical reasoning
for everyday life.

Read Chapters 5 and 6

Document/Other

Reference

Instruction

Chapter 5 Review
Questions
.ncu.edu/Week/WeekDetail?weekid=12858&learnerCourseId=404628″ title=”Download”>Chapter 5
PowerPoint.ppt.ppt

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Chapter 6 Review
Questions
.ncu.edu/Week/WeekDetail?weekid=12858&learnerCourseId=404628″ title=”Download”>Chapter 6
PowerPoint.ppt.ppt

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Lecture week 4: Activity Description
After you complete the
textbook readings, check your understanding of the main concepts by reviewing
the chapter review questions in the attached PowerPoint files. Be sure to
revisit appropriate sections of the textbook if you find that you need more
review. While these questions are not a graded part of this assignment, they are
important because they will help you monitor your learning as you progress
through the course.

Assignment
Instruction week 4: Week 4 Assignment: Complete Application Questions and Problems

Activity Description
Download.ncu.edu/syllabus/download_file.asp?syllabus_rr_id=178897″>Data File 3 and complete the problems and questions as
presented. Show your work (either your hand calculations or your statistical
program output). You may either scan your handwritten work and submit it as a
low-resolution graphic, type your answers directly into the document, or cut
and paste your work into a Word file. Be sure to name the file using the proper
NCU naming conventions before its submittal.

Support your paper with a minimum of three (3) scholarly resources. In addition
to these specified resources, other appropriate scholarly resources, including
older articles, may be included.

Length: 5-7 pages not including title and reference pages, may include
spreadsheets.

Your response should demonstrate thoughtful consideration of the ideas and
concepts that are presented in the course and provide new thoughts and insights
relating directly to this topic. Your response should reflect scholarly writing
and current APA standards where appropriate. Be sure to adhere to Northcentral
University’s Academic Integrity Policy.Chapter Five1) If light bulbs have lives that are normally distributed with a mean of 2500 hours and astandard deviation of 500 hours, what percentage of light bulbs have a life less than 2500hours?2) The lifetimes of light bulbs of a particular type are normally distributed with a mean of370 hours and a standard deviation of 5 hours. What percentage of bulbs have lifetimesthat lie within 1 standard deviation of the mean on either side?3) The amount of Jens monthly phone bill is normally distributed with a mean of $60 and astandard deviation of $12. Fill in the blanks:68% of her phone bills are between $______________ and $______________.4) The amount of Jens monthly phone bill is normally distributed with a mean of $50 and astandard deviation of $10. Find the 25th percentile.5) The diameters of bolts produced by a certain machine are normally distributed with amean of 0.30 inches and a standard deviation of 0.01 inches. What percentage of boltswill have a diameter greater than 0.32 inches?6) The annual precipitation amounts in a certain mountain range are normally distributedwith a mean of 88 inches, and a standard deviation of 10 inches. What is the likelihoodthat the mean annual precipitation during 25 randomly picked years will be less than 90.8inches?7) A final exam in Statistics has a mean of 73 with a standard deviation of 7.73. Assumethat a random sample of 24 students is selected and the mean test score of the sample iscomputed. What percentage of sample means are less than 70?8) A mean score on a standardized test is 50 with a standard deviation of 10. Answer thefollowinga. What scores fall between 1 and +1 standard deviation?b. What percent of all scores fall between 1 and +1 standard deviation?c. What score falls at +2 standard deviations?d. What percentage of scores fall between +1 and +2 standard deviations?Show all workChapter Six1) For the following questions, would the following be considered significant if itsprobability is less than or equal to 0.05?a. Is it significant to get a 12 when a pair of dice is rolled?b. Assume that a study of 500 randomly selected school bus routes showed that 480arrived on time. Is it significant for a school bus to arrive late?2) If you flip a coin three times, the possible outcomes are HHH, HHT, HTH, HTT, THH,THT, TTH, and TTT. What is the probability of getting at least one head?3) A sample space consists of 64 separate events that are equally likely. What is theprobability of each?4) A bag contains 4 red marbles, 3 blue marbles, and 7 green marbles. If a marble israndomly selected from the bag, what is the probability that it will be blue?5) The data set represents the income levels of the members of a country club. Estimate theprobability that a randomly selected member earns at least $98,000.112,000112,00086,000119,000126,00098,000105,00098,00090,00082,000140,000154,000133,000147,00094,00078,00094,000182,000126,000119,0006) Suppose you have an extremely unfair coin: The probability of a head is and theprobability of a tail is . If you toss the coin 32 times, how many heads do you expect tosee?7) The following table is from the Social Security Actuarial Tables. For each age, it givesthe probability of death within one year, the number of living out of an original 100,000and the additional life expectancy for a person of that age. Determine the following usingthe table:a. To what age may a female of age 60 expected to live on the average? To whatage is a male of age 70 expected to live on average?b. How many 60-year old females on average will be living at age 61? How many70-year old males on average will be living at age 71?Age1020MALESP(Death Numberwithinofone year) LivingFEMALESLifeP(Death Number LifeExpectancy withinofExpectancyone year) Living0.00011 99,02110.001287 98,45165.130.000105 99,21770.2255.460.000469 98,95060.40304050600.0013750.0025420.0056960.01226397,11395,42791,85384,69246.1636.8828.0920.0070800.028904 70,2140.07168 44,27270.18864 12,862412.987.430.0006270.0014980.0032400.0077400.0189380.0495273.680.146696 24,3319098,43197,51395,37890,84750.6941.1131.9123.2180,583594,3115.459.004.45