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 reference states that average daily high temperature in June in a particular city is 86°F with a standard deviation of 7, and it can be assumed that they to follow a normal distribution. We use the following equation to convert "F (Fahrenheit) to "C(Celsius) C-(F-32)=² (a) Write the probability model for the distribution of temperature in C in June in this city. (Round your standard deviation to four decimal places) ~~-[ (b) What is the probability of observing a 31°C (which roughly corresponds to 87.) temperature or higher a a randemily selected day in June in this city? Calculate using the "C model from part (a). (Round your answer to four decimal places.) (c) The probability of observing a 67.8°F temperature or higher on a randomly selected day in June this city is approximately 0.3983, Did you get the same answer or a different answer in part (b)? Are you surprised? Explain. Both sets of calculations produced approximately the same answer which isn't surprising since once we…
The length of a movie file that is available for streaming is modeled using the normal distribution shown below
Attempt if you know the exact answer,wrong answer will be downvoted and reported.
Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 236 feet and a standard deviation of 44 feet. We randomly sample 49 fly balls. Part (a) If X =average distance in feet for 49 fly balls, then give the distribution of X. Round your standard deviation to two decimal places. X ____, ________,_______ ~ . Part (b) What is the probability that the 49 balls traveled an average of less than 226 feet? (Round your answer to four decimal places.)Sketch the graph. Scale the horizontal axis for X. Shade the region corresponding to the probability. Part (c) Find the 70th percentile of the distribution of the average of 49 fly balls. (Round your answer to two decimal places.) ft †
A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 206.8 cm and a standard deviation of 0.5 cm. Find the probability that the length of a randomly selected steel rod is greater than 208.4 cm. P(x > 208.4 cm) = P(z > Shade: Left of a value Click and drag the arrows to adjust the values. -4 -3 -2 -1 2. -1.5
The average lifetime of a certain tire is 35,000 miles, and the standard deviation is 3,500 miles. Part 1 of 3 If we assume that the mileages model is a normal distribution, what percentage of all such tires will last between 28,000 and 45,500 miles? Show your work. (Use the Empirical Rule.)
Suppose the masses of a batch of 2000 potatoes have a mean of 60 grams with a standard deviation of 8 grams. Assuming the weights have a normal distribution, predict the number of potatoes that would have masses between 45 and 55 grams. Sketch the distribution curve, shade the required probability, and show horizontal scales the population parameters and the z-scores. Solve the problem
This is for statistics
A recent study found that the average length of caterpillars was 2.8 centimeters with a standard deviation of 0.7 centimeters. Assuming that the lengths of all caterpillars is normally distributed, what is the probability that a randomly selected caterpillar will have a length longer than (greater than) 4.0 centimeters? P(x > 4.0 cm) = ___________ Type in your final decimal solution for the probability rounded to four decimal places.
A class is given an exam. The distribution of the scores is normal. The mean score is 78 and the standard deviation is 11. Determine the test score, c such that the probability of a student having a score greater than c is 46%. P(x>c)=0.46
Part 1. The central limit theorem only applies when the original distribution is normal. True or false? Part 2. The shape of the t distribution is impacted by the size of the sample used to generate it. True or false?
Assume that females have pulse rates that are normally distributed with a mean of μ=74.0 beats per minute and a standard deviation of σ=12.5 beats per minute. Complete parts (a) through (c) below. Question content area bottom Part 1 a. If 1 adult female is randomly selected, find the probability that her pulse rate is between 67 beats per minute and 81 beats per minute. The probability is 0.42450.4245. (Round to four decimal places as needed.) Part 2 b. If 4 adult females are randomly selected, find the probability that they have pulse rates with a mean between 67 beats per minute and 81 beats per minute. The probability is enter your response here. (Round to four decimal places as needed.)

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