Applying the Normal Distribution and Central Limit TheoremThe population of adult women in the United States has a mean height of 65 inches (5'5") and a standarddeviation of 3.5 inches.Let X = the height of an American female.Thus, X~ N(65, 3.5).Use the scenario above to determine the selected probabilities below. You may wish to use the NormalDistribution Calculator hosted by the University of lowa's Department of Mathematical Sciences.Remember: the formatting of this calculator may vary slightly from what is used in class. (link: NormalDistribution Calculator)a. What is the probability of randomly selecting a female shorter than 58 inches tall?P(X<58) =(Include five decimal places.)b. Determine the 90th percentile for the distribution. (This Normal Distribution Percentile Calculatormay be useful.)x =inches. (Include one decimal place.)c. If 100 women were randomly chosen, what is the probability that the sample mean of this groupwould be less than 64.5 inches?P(X < 64.5)(Include five decimal places.)=

Let X denotes the height of an American female X~N(65, 3.5)We have to finda..the probability of…

Answered: Applying the Normal Distribution and…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A Show Time Remaining A The body lengths of deer mice are known to vary approximately normally, with mean 86 mm and standard deviation 8 mm. A research group is interested whether vitamin supplements will increase deer mouse body length. They select a random sample of 100 deer mice from the population of all deer mice that would ever receive vitamin supplements and observe their body lengths. Suppose the sample mean is calculated as 87.2 mm. Let u be the mean body length of deer mice who receive vitamin supplements. Provide the null and alternative hypotheses most appropriate for this situation. O A. Ho: H = 86 vs. Ha: P> 86 B. Họ: H = 87.2 vs. Hạ: µ 87.2 Reset Selection
Let X = number of miles a family travels for summer vacation. X follows a normal distribution with a mean of 311 miles and standard deviation of 232 miles. If a family traveled 600 miles, how many standard deviations are they away from the mean? Calculate the following probabilities
The length of a movie file that is available for streaming is modeled using the normal distribution shown below
Assume that adults have IQ scores that are normally distributed with a mean of μ=105 and a standard deviation σ=20. Find the probability that a randomly selected adult has an IQ between 93 and 117.
Accordi the historical data, the life expectancy in Mexico is equal to the life expectancy in Spain. A new study has been made to see whether this has changea. Records of 205 individuals from Mexico who died recently are selected at random. The 205 individuals lived an average of 71.8 years with a standard deviation of 2.6 years. Records of 250 individuals from Spain who died recently are selected at random and independently. The 250 individuals lived an average of 71.2 years with a standard deviation of 3.0 years. Assume that the population standard deviation of the life expectancy can be estimated by the sample standard deviations, since the samples that are used to compute them are quite large. At the 0.05 level of significance, is there enough evidence to support the claim that the life expectancy, H1, in Mexico is not equal to the life expectancy, µ,, in Spain anymore? Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to at least three…
The mean is 146 and the standard deviation is 35. A score of 41 is how many z-scores below the mean?
Assume the samples are random and independent, the populations are nomally distributed, and the population variances are equal. The table available below shows the prices (in dollars) for a sample of automobile batteries. The prices are classified according to battery type. At a = 0.10, is there enough evidence to conclude that at least one mean battery price is different from the others? Complete parts (a) through (e) below. E Click the icon to view the battery cost data. (a) Let u. 2 Ha represent the mean prices for the group size 35, 65, and 24/24F respectively. Identify the claim and state Ho and H.. Ho: H - X Cost of batteries by type The claim the V hypothesis. Group size 35 Group size 65 Group size 24/ 24F 91 99 111 119 126 O 91 144 174 180 278 79 84 126 140 140 (b) Find the critical value, Fo. and identify the rejection region. The rejection region is F Fo, where Fo- (Round to two decimal places as needed.) (c) Find the test statistic F. F= (Round to two decimal places as…
Assume the samples are random and independent, the populations are nomally distributed, and the population variances are equal. The table available below shows the prices (in dollars) for a sample of automobile batteries. The prices are classified according to battery type. At a = 0.10, is there enough evidence conclude that at least one mean battery price is different from the others? Complete parts (a) through (e) below. E Click the icon to view the battery cost data. (a) Let u1. P2. H3 represent the mean prices for the group size 35, 65, and 24/24F respectively. Identify the claim and state Ho and H. H Cost of batteries by type The claim is the V hypothesis. Group size 35 Group size 65 Group size 24/24F 101 111 121 124 D 146 173 182 278 124 140 141 89 (b) Find the critical value, Fo, and identify the rejection region. 90 79 84 The rejection region is F Fo, where Fo = (Round to two decimal places as needed.) (c) Find the test statistic F. Print Done F= (Round to two decimal places as…
Systolic blood pressure readings are normally distributed with a mean of 121 and standard deviation of 15. If a person from the population was selected at random, find the probability that their blood pressure is in the acceptable range (between 114 and 140) for an athletic activity. A. Label and shade the normal distribution curve to model this problem.
A surgery has a success rate of 90%. Suppose that the surgery is performed on threepatients Graph the probability distribution for X using a histogram.Find the mean of X.Find the variance and standard deviation of X.
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