Data TablesTable of the numbers of hits for 25 games1 2 12 3 3 3 32 125 1 1 22Table of the numbers of hits for 50 gamesO0 1213 313 2 5 1223 4 1 0 2 0 2 0 2 12 2 1 12 3 320|0|1|0|2|2|2 3 1 1 3 2 The probability distribution of the random variable X represents the number of hits a baseball player obtained in a game for the 2012 baseball season.13X 024 5P(x) 0.1671 0.3335 0.2777 0.1482 0.0380 0.0355The probability distribution was used along with statistical software to simulate 25 repetitions of the experiment (25 games). The number of hits was recorded. Approximate the mean and standarddeviation of the random variable X based on the simulation. The simulation was repeated by performing 50 repetitions of the experiment. Approximate the mean and standard deviation of the randomvariable. Compare your results to the theoretical mean and standard deviation. What property is being illustrated?Click the icon to view the data tables.Compute the theoretical mean of the random variable X for the given probability distribution.Hx= 1.663 hits(Round to three decimal places as needed.)Compute the theoretical standard deviation of the random variable X for the given probability distribution.x = 1.228 hits(Round to three decimal places as needed.)Approximate the mean of the random variable X based on the simulation for 25 games.X 1.96 hits(Round to three decimal places as needed)Approximate the standard deviation of the random variable X based on the simulation for 25 games.S≈ hits(Round to three decimbs places as needed.)A

Answered: Image /qna-images/answer/2143cfe8-2276-4927-ad99-2799a8d4e501.jpg

Answered: The probability distribution of the…

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 physical fitness association is including the mile run in its secondary school test. the time for this event for girls in the secondary school is known to posses a normal distribution with the mean of 450 seconds and standard deviation of 59 seconds. find the probability that a randomly selected girl in secondary school will take longer than 335 seconds to run the mile A. 0.5107 B. 0.9893 c. 0.0107 D. 0.4893
Measuring success as the ratio of runs/at-bats makes sense. Suppose the mean ratio for the league is 0.200 and is normally distributed with a standard deviation of 0.01. How could a manager apply the normal probability distribution (for recruiting) to determine if it is unusual that a random player has a ratio of 0.220?
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
Find the probability that the average amount paid by the sample of households exceeds $50.
A union of restaurant and foodservice workers would like to estimate the mean hourly wage, μ, of foodservice workers in the U.S. The union will choose a random sample of wages and then estimate μ using the mean of the sample. What is the minimum sample size needed in order for the union to be 90% confident that its estimate is within $0.50 of μ? Suppose that the standard deviation of wages of foodservice workers in the U.S. is about $2.20. Carry your intermediate computations to at least three decimal places. Write your answer as a whole number (and make sure that it is the minimum whole number that satisfies the requirements). (If necessary, consult a list of formulas.)
Women's shoe sizes are (approximately) normally distributed, with an average size of 8.076 and a standard deviation of 1.468. You work at Vogue Magazine, and would like to interview some women about how shoes fit. You take a random sample of 10 women. What is the probability that the 10 women you sampled had an average shoe size that is greater than 8?
Find the probability that the mean volume of soft drink in the 25 sampled bottles is less than 15.4 ounces. (Give your answer to four decimal places) Find the probability that the mean volume of soft drink in the 25 sampled bottles is more than 15.5 ounces. (Give your answer to four decimal places)
Women's shoe sizes are (approximately) normally distributed, with an average size of 8.076 and a standard deviation of 1.468. You work at Vogue Magazine, and would like to interview some women about how shoes fit. You take a random sample of 10 women. What is the probability that the 10 women you sampled had an average shoe size that is less than 8?
Cody took his first physics exam and scored an 80. The population mean for this exam is 70, and the standard deviation is 5. What is the probability of selecting a person with a score greater than Cody’s?
Cans of regular Coke are labeled as containing 12 oz. Statistics students weighed the contents of 8 randomly chosen cans, and found the mean weight to be 12.13 ounces. Assume that cans of Coke are filled so that the actual amounts are normally distributed with a mean of 12.00 oz and a standard deviation of 0.11 oz. Find the probability that a sample of 8 cans will have a mean amount of at least 12.13 oz.
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.
The full height of a certain species of tree has a normal probability distribution with a mean of 195.6 ft and a standard deviation of 7.5 ft. State the random variable. ¯x = the height of a certain species of tree ¯x = the mean height of a certain species of tree x = the height of a certain species of tree x = the diameter of a certain species of tree A tree of this type grows in my backyard, and it stands 187.4 feet tall. Find the probability that the height of a randomly selected tree is shorter than mine. Round to three decimal places.Which is the notation for the probability that the height is shorter than mine? P(x < 187.4) P(¯x < 195.6) P(¯x > 195.6) P(x > 195.6) P(¯x< 187.4) P(x < 195.6)

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