File Name: normal distribution examples and solutions .zip
Since a continuous random variable can take any value within its range, we cannot list all the possible values and their probabilities as in the discrete case. For instance the rate of inflation could be recorded to any number of decimal places so it is impossible to list all possible inflation rates. For continuous random variables we represent probabilities using a probability density function pdf sometimes just called the probability distribution. Below is an example of what a pdf might look like. In general, calculating the expected value mean and variance of a continuous random variable requires using integration not covered here.
These are homework exercises to accompany the Textmap created for "Introductory Statistics" by OpenStax. Use the following information to answer the next two exercises: The patient recovery time from a particular surgical procedure is normally distributed with a mean of 5. The length of time to find a parking space at 9 A. If the mean is significantly greater than the standard deviation, which of the following statements is true?
The heights of the National Basketball Association players were listed on team rosters at the start of the — season. For each of the following heights, calculate the z -score and interpret it using complete sentences.
Systolic blood pressure for males follows a normal distribution. Which of the following is the best interpretation of this standardized score? The World Health Organization measures child development by comparing the weights of children who are the same height and the same gender.
Weights are normally distributed. Calculate the z -scores that correspond to the following weights and interpret them. In , 1,, students heading to college took the SAT. Use the following information to answer the next three exercises: The length of time it takes to find a parking space at 9 A.
Based upon the given information and numerically justified, would you be surprised if it took less than one minute to find a parking space? Find the probability that it takes at least eight minutes to find a parking space. Seventy percent of the time, it takes more than how many minutes to find a parking space?
According to a study done by De Anza students, the height for Asian adult males is normally distributed with an average of 66 inches and a standard deviation of 2. Suppose one Asian adult male is randomly chosen. IQ is normally distributed with a mean of and a standard deviation of Suppose one individual is randomly chosen.
The percent of fat calories that a person in America consumes each day is normally distributed with a mean of about 36 and a standard deviation of Suppose that one individual is randomly chosen. Suppose that the distance of fly balls hit to the outfield in baseball is normally distributed with a mean of feet and a standard deviation of 50 feet.
In China, four-year-olds average three hours a day unsupervised. Most of the unsupervised children live in rural areas, considered safe. Suppose that the standard deviation is 1. We randomly select one Chinese four-year-old living in a rural area. We are interested in the amount of time the child spends alone per day. The standard deviation was There are only 40 election districts in Alaska.
The distribution of the votes per district for President Clinton was bell-shaped. Suppose that the duration of a particular type of criminal trial is known to be normally distributed with a mean of 21 days and a standard deviation of seven days. Terri Vogel, an amateur motorcycle racer, averages The distribution of her race times is normally distributed.
We are interested in one of her randomly selected laps. Table displays the ordered real data in minutes :. Suppose that Ricardo and Anita attend different colleges. In complete sentences, explain why each of the following statements may be false. Table shows a sample of the maximum capacity maximum number of spectators of sports stadiums. The table does not include horse-racing or motor-racing stadiums. An expert witness for a paternity lawsuit testifies that the length of a pregnancy is normally distributed with a mean of days and a standard deviation of 13 days.
An alleged father was out of the country from to days before the birth of the child, so the pregnancy would have been less than days or more than days long if he was the father. The birth was uncomplicated, and the child needed no medical intervention. What is the probability that he was NOT the father? What is the probability that he could be the father? Calculate the z -scores first, and then use those to calculate the probability.
A NUMMI assembly line, which has been operating since , has built an average of 6, cars and trucks a week. Let X represent the number of defective cars in the sample. What can we say about X in regard to the Assume a normal distribution for the defective cars in the sample. Solve the following:. Facebook provides a variety of statistics on its Web site that detail the growth and popularity of the site. On average, 28 percent of 18 to 34 year olds check their Facebook profiles before getting out of bed in the morning.
Suppose this percentage follows a normal distribution with a standard deviation of five percent. The data cannot follow the uniform distribution.
The data cannot follow the exponential distribution.. The data cannot follow the normal distribution. Explain your answer. The height of 77 inches is 0. An NBA player whose height is 77 inches is shorter than average. The height 85 inches is 1. An NBA player whose height is 85 inches is taller than average. There are very few NBA players this tall so the answer is no, not likely.
Calculate the z -scores for the male systolic blood pressures and millimeters. If a male friend of yours said he thought his systolic blood pressure was 2. Interpret it using a complete sentence. What math SAT score is 1. What can you say about this SAT score? For , the SAT math test had a mean of and standard deviation The ACT math test is an alternate to the SAT and is approximately normally distributed with mean 21 and standard deviation 5.
If one person took the SAT math test and scored and a second person took the ACT math test and scored 30, who did better with respect to the test they took? The exam score of With respect to the test they took, the person who took the ACT did better has the higher z -score. Yes No Unable to determine. Include a sketch of the graph, and write a probability statement. Would you expect to meet many Asian adult males over 72 inches? Explain why or why not, and justify your answer numerically.
Sketch the graph, and write the probability statement. Sketch the graph and write the probability statement. Graph the situation. Shade in the area to be determined. Find the maximum number for the lower quarter of percent of fat calories. Sketch the graph. Scale the horizontal axis X. Shade the region corresponding to the probability. Find the probability. Find the 80 th percentile of the distribution of fly balls. What percent of the children spend over ten hours per day unsupervised?
Seventy percent of the children spend at least how long per day unsupervised? The probability that a child spends over ten hours a day unsupervised is less than 0. Is 1, How do you know? Find the probability that a randomly selected district had fewer than 1, votes for President Clinton. Find the probability that a randomly selected district had between 1, and 2, votes for President Clinton. Find the third quartile for votes for President Clinton.
Sixty percent of all trials of this type are completed within how many days? Table displays the ordered real data in minutes : 0. Construct a histogram. Draw a smooth curve through the midpoints of the tops of the bars.
Problems and applications on normal distributions are presented. The solutions to these problems are at the bottom of the page. Also an online normal distribution probability calculator may be useful to check your answers. Free Mathematics Tutorials. About the author Download E-mail. Normal Distribution Problems with Solutions Problems and applications on normal distributions are presented. For a certain type of computers, the length of time bewteen charges of the battery is normally distributed with a mean of 50 hours and a standard deviation of 15 hours.
Documentation Help Center Documentation. The normal distribution, sometimes called the Gaussian distribution, is a two-parameter family of curves. The usual justification for using the normal distribution for modeling is the Central Limit theorem, which states roughly that the sum of independent samples from any distribution with finite mean and variance converges to the normal distribution as the sample size goes to infinity. Create a probability distribution object NormalDistribution by fitting a probability distribution to sample data fitdist or by specifying parameter values makedist. Then, use object functions to evaluate the distribution, generate random numbers, and so on. Work with the normal distribution interactively by using the Distribution Fitter app. You can export an object from the app and use the object functions.
be able to use tables of the normal distribution to solve problems;. • be able to use the You should note that the accuracy of your solutions will depend on the tables (or graphic the mean, you need to know the p.d.f. This was first discovered.
When people think about modern statistics, they often think about the immense advancements in the realm of machine learning and artificial intelligence. While self-driving cars and robots are incredible uses of science and maths, the majority of the statistics that are used on a daily basis are really quite simple. Frequency, a descriptive statistic, is one example of this. Frequency is defined as the number of times something occurs.
We use upper case variables like X and Z to denote random variables , and lower-case letters like x and z to denote specific values of those variables. Whenever you measure things like people's height, weight, salary, opinions or votes, the graph of the results is very often a normal curve. A random variable X whose distribution has the shape of a normal curve is called a normal random variable.
A probability distribution is a statistical function that describes the likelihood of obtaining the possible values that a random variable can take. By this, we mean the range of values that a parameter can take when we randomly pick up values from it. Suppose in a city we have heights of adults between the age group of years ranging from 4. But if we have the distribution of heights of adults in the city, we can bet on the most probable outcome.
Свет внутри исходил лишь от светящихся компьютерных мониторов Стратмора. - Коммандер! - повторила. - Коммандер.
Сьюзан не могла не восхититься умом Танкадо. Не открыв своего алгоритма, он доказал АНБ, что тот не поддается дешифровке. Стратмор протянул Сьюзан газетную вырезку. Это был перевод рекламного сообщения Никкей симбун, японского аналога Уолл-стрит джорнал, о том, что японский программист Энсей Танкадо открыл математическую формулу, с помощью которой можно создавать не поддающиеся взлому шифры.
Теперь Сьюзан точно знала, зачем ее вызвал Стратмор. - Я, кажется, догадалась, - сказала. - Вы хотите, чтобы я проникла в секретную базу данных ARA и установила личность Северной Дакоты. Стратмор улыбнулся, не разжимая губ.
Нареченный Детским манежем, Третий узел ничем не напоминал стерильную атмосферу остальной части шифровалки. Его обстановка напоминала домашнюю - мягкий ковер, высокотехнологичная звуковая система, холодильник, полный напитков и всяческой еды, маленькая кухня и даже баскетбольное кольцо. В отношении шифровалки в АНБ сложилась своеобразная философия.
ГЛАВА 122 - Шесть минут! - крикнул техник. Сьюзан отдала приказ: - Перепечатайте сверху. Нужно читать по вертикали, а не по горизонтали. Пальцы Соши стремительно забегали по клавишам.
- Сэр, мне кажется… что с ТРАНСТЕКСТОМ какая-то проблема. Стратмор закрыл дверцу холодильника и без тени волнения взглянул на Чатрукьяна. - Ты имеешь в виду работающий монитор. Чатрукьян растерялся.
Сколько там этих сироток? - спросила. Соши развела руками. Она села за терминал Джаббы и перепечатала все группы, а закончив, подбежала к Сьюзан. Все посмотрели на экран. PFEE SESN RETM MFHA IRWE ENET SHAS DCNS IIAA IEER OOIG MEEN NRMA BRNK FBLE LODI Улыбалась одна только Сьюзан.
Время ввода - двадцать три тридцать семь и восемь секунд, однако время завершения дешифровки не указано. - Мидж полистала страницы.
These are homework exercises to accompany the Textmap created for "Introductory Statistics" by OpenStax.Trinette T. 23.03.2021 at 07:33
Scores on the GMAT are roughly normally distributed with a mean of and a standard deviation of What is the probability of an individual scoring above.Takara C. 26.03.2021 at 09:13
This guide will show you how to calculate the probability area under the curve of a standard normal distribution.Ewan W. 26.03.2021 at 18:51
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Data are said to be normally distributed if their frequency histogram is apporximated by a bell shaped curve.