Finding Probabilities in Normal DistributionsStatistician Jim Albert compiled data about every pitch thrown by 20 starting pitchers during the 2009 MLBseason. The data set included the type of pitch thrown (curveball, changeup, slider, etc.) as well as thespeed of the ball as it left the pitcher's hand. The data showed that the speeds of the fastballs arenormally distributed with mean 92.12 mph and standard deviation 2.43 mph.(a) Compute the z-score of the fastball with speed 89.6 mph. Round your answer to two decimal places.(b) What percentage of these fastballs would you expect to have speeds between 89.2 mph and 93 mph?Express your answer as a decimal. Round to three decimal places.(c) What percentage of these fastballs would you expect to have speeds above 93 mph? Express youranswer as a decimal. Round to three decimal places.(d) Finding Values: A baseball fan wishes to identify the fastballs among the fastest 21% of all such pitches.Above what speed must a fastball be in order to be included in the fastest 21%? Round your answer to thenearest 0.1 mph.mphQuestion Help: Message instructorSubmit Question

GivenMean(μ)=92.12standard deviation(σ)=2.43

Answered: Finding Probabilities in Normal…

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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The football coach randomly selected fifteen players and timed how long each player took to perform a certain drill. The times (in minutes) were: 3.5, 3.3, 3.2, 4.7, 4.4, 3.5, 3.9, 4.5, 4.8, 5.2, 5.4, 4.0, 4.3, 4.1, 5.1 (a) Show that this data approximates a normal distribution. (b) Determine a 90% confidence interval for the mean time for all players.
A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. If 64 applications are randomly selected, what is the probability that the mean credit rating of these 64 applicants will be between 205 and 275. (Round your answer to 4 decimal places.) (Calculator: http://statisticshelper.com/normal-distribution-calculator) A. 0.5011 B. 0.4113 C. 0.2119 D. 0.3664
A waiterbelieves the distribution of his tips has a model that is slightly skewed to the left, with a mean of $8.60 and a standard deviation of $4.20. He usually waits on about 50 parties over a weekend of work. a) Estimate the probability that he will earn at least $450. b) How much does he earn on the best 5% of such weekends?
A 1 6. Height (om) 2 179 3 174 4 156 171 6. 170 7 165 8. 170 157 10 155 11 157 12 177 13 172 14 154 15 155 16 158 17 170 18 174 19 170 20 154 21 172 22 164 23 173 24 164 25 172 26 173 27 150 28 150 29 160 30 150 31 166
Gas mileage of vehicles follows a normal curve. A Ford Escape claims to get 25 mpg highway, with a standard deviation of 1.6 mpg. A Ford Escape is selected at random. (a) What is the probability that it will get more than 28 mpg? 1b. Suppose the test scores among a set of first year nursing students are normally distributed with a mean of 500 and a standard deviation of 100. If a student nurse scores a 700, what would be her z-score?
The diameter of a brand of tennis balls is approximately normally distributed with a mean of 2.5 inches and a standard deviation of 0.5 inches. A random sample of 50 ping-pong balls is selected. The probability is 0.70 that the sample mean will be between what two values (symmetrically centered on the population mean)?
A triathlon consisting of swimming, cycling, and running is one of the more strenuous amateur sporting events. An article reports on a research study involving nine male triathletes. Maximum heart rate (beats/min) was recorded during performance of each of the three events. For swimming, the sample mean and sample standard deviation were 187.0 and 7.2, respectively. Assuming that the heart-rate distribution is (approximately) normal, construct a 98% CI for true mean heart rate of triathletes while swimming. (Round your answers to one decimal place.) USE SALT beats/min You may need to use the appropriate table in the Appendix of Tables to answer this question.
Scores of each of the Knitting Aptitude tests were normally distributed with a mean of 6 hours and a standard deviation of 1.67 hours. Carrie will be taking the test tomorrow. Assume the data is normally distributed. Determine the probability of someone finishing in less than 2.17 hours 0.9891 0.5000 1.0 0.0109
The Aluminum Association reports that the average American uses 56.8 pounds of aluminum in a year. A random sample of 50 households is monitored for one year to determine aluminum usage. If the population standard deviation of annual usage is 12.3 pounds, what is the probability that the sample mean will be each of the following? Appendix A Statistical Tables d. Less than 55 poundse. Less than 49 pounds
The patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.65.6 days and a standard deviation of 2.12.1 days. What is the probability of spending more than two days in recovery? A.) 0.9568 B.) 0.0432 C.) 0.8922 D.) 0.0401
The Aluminum Association reports that the average American uses 56.8 pounds of aluminum in a year. A random sample of 50 households is monitored for one year to determine aluminum usage. If the population standard deviation of annual usage is 12.3 pounds, what is the probability that the sample mean will be each of the following? Appendix A Statistical Tables a. More than 60 poundsb. More than 56 poundsc. Between 55 and 57 pounds
Motovolla is producing batteries for cell phones. A study revealed that while using a cell phone constantly the new batteries lasted an average of 250 minutes with a standard deviation of 10 minutes. The data also appeared to be normally distributed. What percent of the batteries lasted less than 4 hours (240 minutes)? 信 54.15 34 1N 13.6% 136N O a) 84.1% O b) 97.7% O ) 15.9% O d) 47.7%

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