Apply Probability, Sampling Distributions, and Inference 8 NORTHCENTRAL UNIVERSITY Student: RodgersGBTM7104-8 Academic Integrity: As doctoral student in the field of Organizational Leadership with leadership development, I was given the challenge for this week 3 assignment, which we are asked to observe the chapter readings (Chapters 5 and 6) for this week, which are critical as they introduce and explain the real concepts of probability, and the normal distribution. The instruction of week 3 task explains how in our daily lives most results are represented as probabilistic (a view of possibility or profitability), and the failure to have definitive (conclusive or final), and the absolutes involvement. This is where our assignment in the reading, can help us check our understanding of the main concepts by reviewing the chapter review questions (Dr. Halawi, 2016). BTM7104-8 Dr. Leila Halawi Apply Probability, Assignment Week 3 Apply Probability, Sampling Distributions, and Inference 8 I am face with yet another challenge of observing collective data to continue developing and practicing the skills needed to complete a comprehensive literature review as the \"Activity Description: This week 3 assignment request that we do the completion by gaining the proficiency (the ability or skill) in understanding and apply the following requirements in the concepts and processes such as below: Normal distribution. The 68-95-99.7 rule. Determining the areas under the normal distribution. How z-scores are used to standardize the scores. How z-scores can be transposed (moved or rearranged) into the percentile rankings The law of the large numbers. The vulnerability (helplessness, or weakness) to error of the probability. The Calculating probability (Dr. Halawi, 2016). o For example: this is where, I must also apply my new knowledge by answering questions and solving problems that correspond to the reading assignment. Assignment Preparation: This course request that each person \"download the Data File 3, and complete the problems and the questions given in the exercise as presented, such as below (Dr. Halawi, 2016): Learning Outcomes: For example: o In this case, we as instructed to Show all work (which also means including any statistical program output that was used to answer a problem/question). o Unless otherwise, we are requested, to please submit all our work and the assignments (with your answers along with the assignment questions/problems) in Word file format. Apply Probability, Sampling Distributions, and Inference 8 o Be sure to name the file using the proper NCU naming conventions before its submittal. o This is where my submittal 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. Faculty Use Only Student: RodgersGBTM7104-8 Apply Probability, Sampling Distributions, and Inference 8 Course Code: BTM7104-8 Course Start Date: 11/07/2016 Professor: Dr. Leila Halawi Section: Introduction to Statistics Week: 3 Activity: Apply Probability, Sampling Distributions, and Inference Activity Due Date: 11/27/2016 Introduction This is where \"Normal Distribution,\" is a part of \"Rudimentary (undeveloped, basic, fundamental, and the primary) probability theory,\" which is the primary focus of this section. Our week 3 assignment on the topic instructions; explains how many situations are based on Apply Probability, Sampling Distributions, and Inference 8 probabilistic (Possibility focus) reasoning and the occurrences (amounts, rates, frequencies, numbers of things and the incidences). It explains how important it is to understand the probability theory and it's the real connection to statistics (Figures, information's, and digits). For example, it talks about the choosing a life insurance policy that is now the decision, which is influenced heavily by the probability theory (Dr. Halawi, 2016). Nevertheless, the studying in this case, observe the fundamental statistical concept that will not only support a person like me, scholarly academic goals; but it will be also the help a person like me, can use to understand how the probability can be used in more influences with most decisions made in everyday life (Dr. Halawi, 2016). In this section my study will demonstrate to viewers how we can examine the important statistical concept of the probability distribution as well. We will observe the many forms of data analysis develop in the concept, along with many types of elements that can be viewed in our daily everyday lives, which can be extrapolated (help draw conclusions) from probability distribution (Dr. Halawi, 2016). For example, earlier the course mention how there are the 68-95-99.7 percent rule, and how the central limit theorem (formula, hypothesis, proposal, statement, and proposition) Apply Probability, Sampling Distributions, and Inference 8 will be introduced, along with the required standard deviation and how it relates to the \"normal probability distribution (Dr. Halawi, 2016). In this case, there were additional concepts that was more important, which were found in this section of week 3 assignment that would include; the normal distribution and the cover, percentiles, standard required scores, along with central limit theorem. This would include the understanding statistical significance, expressing and the calculating the basic probability Data File 3 For example: Show all work Chapter Five 1) If light bulbs have lives that are normally distributed with a mean of 2500 hours and a standard deviation of 500 hours, what percentage of light bulbs have a life less than 2500 hours? This is where a researcher like me would calculate the z-score method for this mathematic question basic on the probability. The answer would come from the probability and the statistics formula in this case, would be standard deviation in the compact form. These are the given answer that was found: According to examples that represent earlier in the week 3 assignment there were 68-95-99.7 that can be applied in probability for the following (Dr. Halawi, 2016): Approximately (when it's around off to the nearest number) 68% of the light bulbs have a life between - = 2000 and + = 3000 (this is where can be the mean and can be the standard deviation). Apply Probability, Sampling Distributions, and Inference 8 The next approximated figure can be 95% of the light bulbs that have a life between -2 =1500 and + =3500. The next approximated figure would be 99.7% of the light bulbs that have a life between -3 =1000 and +3 =4000. In this case, (99.7%)/2= 49.85% of the light bulbs that have a life inferior (substandard, lower, and lesser than 2500 (which is the mean in this case) This is where the result can be verified by using z-score tables. Indeed, = 2500 and = 500 for the value of 2500 hours, so the z-score would calculate as (2500 -2500)/500 = 0. The z-score table reveals that the corresponding percentile is 50%. This demonstrate that 50% of the light bulbs have a life inferior less than 2500 hours (Northcentral University Data File, 2016). 2) The lifetimes of light bulbs of some types are normally distributed with a mean of 370 hours and a standard deviation of 5 hours. What percentage of bulbs has lifetimes that lie within 1 standard deviation of the mean on either side? Once again, this is where the result 3) The amount of Jen's monthly phone bill is normally distributed with a mean of $60 and a standard deviation of $12. Fill in the blanks: 68% of her phone bills are between $______________ and $______________. 4) The amount of Jen's monthly phone bill is normally distributed with a mean of $50 and a standard deviation of $10. Find the 25th percentile. Apply Probability, Sampling Distributions, and Inference 8 5) The diameters of bolts produced by a certain machine are normally distributed with a mean of 0.30 inches and a standard deviation of 0.01 inches. What percentage of bolts will have a diameter greater than 0.32 inches? 6) The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 88 inches, and a standard deviation of 10 inches. What is the likelihood that the mean annual precipitation during 25 randomly picked years will be less than 90.8 inches? 7) A final exam in Statistics has a mean of 73 with a standard deviation of 7.73. Assume that a random sample of 24 students is selected and the mean test score of the sample is computed. 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 the following a. 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 falls between +1 and +2 standard deviations? Show all work Apply Probability, Sampling Distributions, and Inference 8 Chapter Six 1) For the following questions, would the following be considered \"significant\" if its probability 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 480 arrived 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 the probability of each? 4) A bag contains 4 red marbles, 3 blue marbles, and 7 green marbles. If a marble is randomly selected from the bag, what is the probability that it is blue? 5) The data set represents the income levels of the members of a country club. Estimate the probability that a randomly selected member earns at least $98,000. Apply Probability, Sampling Distributions, and Inference 8 112,000 126,000 90,000 133,000 94,000 112,000 98,000 82,000 147,000 182,000 86,000 105,000 140,000 94,000 126,000 119,000 98,000 154,000 78,000 119,000 6) Suppose you have an extremely unfair coin: The probability of a head is and the probability of a tail is . If you toss the coin 32 times, how many heads do you expect to see? 7) The following table is from the Social Security Actuarial Tables. For each age, it gives the probability of death within one year, the number of living out of an original 100,000 and the additional life expectancy for a person of that age. Determine the following using the table: a. To what age may a female of age 60 expected to live on the average? To what age 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 many 70-year old males on average will be living at age 71? Apply Probability, Sampling Distributions, and Inference 8 MALES FEMALES P (Death Number Life P (Death Number Life within of Expectancy within of Expectancy one year) Living one year) Living 10 0.000111 99,021 65.13 0.000105 99,217 70.22 20 0.001287 98,451 55.46 0.000469 98,950 60.40 30 0.001375 97,113 46.16 0.000627 98,431 50.69 40 0.002542 95,427 36.88 0.001498 97,513 41.11 50 0.005696 91,853 28.09 0.003240 95,378 31.91 60 0.012263 84,692 20.00 0.007740 90,847 23.21 70 0.028904 70,214 12.98 0.018938 80,583 15.45 80 0.071687 44,272 7.43 0.049527 594,31 9.00 90 0.188644 12,862 3.68 0.146696 24,331 4.45 Age Conclusion Apply Probability, Sampling Distributions, and Inference 8 References Bennett, J. O., Briggs, W. L., & Triola, M. F. (2014). Statistical reasoning for everyday life. Read Chapters 5 and 6 Northcentral University (2011). Retrieved, Data File 3, 10000 E. University Dr. Prescott Valley, AZ 86314 USA, from hptt://www.ncu.edu p:928-541-7777 f: 928 541-7817