Practice Question 1:Assume that the height of AUM male students are normally distributed with a mean of 165 cmand a standard deviation of 10 cm.a) Find the probability that a random male height is less than 162 cm.b) Find the probability that a random male height is between 164 and 166 cm.c) What are the height that only 5% of males exceed this height?d) Find the probability that the average height of a random sample of 16 males will be lessthan 165.5.c) Find the probability that the average height of a random sample of 25 males will bebetween 164.5 and 165.5.Why we can apply CLT here?

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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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Suppose the average amount of money that people spend on their pets per month is 47 dollars, with a standard deviation of 6 dollars. For a sample of 36 people, final the average amount of money spent on pets that defines the bottom 30% in the distribution.For a sample of 36 people, what is the probability for this sample’s mean to be higher than 50 dollars.
Suppose you sample one value from a uniform distribution with a = 0 and b = 20. a) What is the probability that the value will be between 13 and 19? b) What is the probability that the value will be between 4 and 9? c) What is the mean? d) What is the standard deviation?
The results of a survey indicates that the time a shopper spends in a supermarket is approximately normally distributed with an average of 45 minutes and a standard deviation of 12 minutes. A shopper enters the store. a) Sketch the distribution. b) Find the probability that the shopper will be in the store for between 9 and 57 minutes. c) Find the probability that the shopper will be in the store for more than 33 minutes. d) 200 shoppers enter the store in the early evening, approximately how many shoppers would be expected to finish shopping in less than one hour and nine minutes?
2. The weights of male basketball players on a certain university are normally distributed with a mean of 180 pounds and a standard deviation of 26 pounds. If a player is selected at random, find the probability that A) the player will weigh more than 225 pounds. B) The player will weigh less than 200 pounds. C) The player will with between 160 and 195 pounds. 3. The average score on one of your MMW exams was 70 with a standard deviation of 15. Assuming the scores are normally distributed. A) If your z-score was 1.5, what is your corresponding score and percentile rank? B) If the z-score associated with a given raw score is equal to 0, what does this imply? C) What percentage of the students got a score above 90? D) What percentage of the students got a score less than 40? E) If the top 5% are given A's in that examination, what is the lowest raw score to get an A?
8) Scores on an exam have a normal distribution with a mean of 125 and a standard deviation of 19. Be sure to draw the normal distribution and shade the are being found. a) Find the probability that a person would score above 129 b) Find the probability that a person would score between 123 and 151. c) Find the probability that a group of 7 people would have a mean score above 130. d) Find the score needed to be in the top 10% of the class.
Scores on a standardized exam for 2nd graders are approximately normally distributed with a mean of 72 and a standard deviation of 6. a) b) c)
Recently, the bowling scores of a certain bowler were normally distributed with mean 202 and standard deviation 19. a) Find the probability that a score is from 185 to 210.b) Find the probability that a score is from 165 to 275.c) Find the probability that a score is greater than 200.d) The best score is 299. Find the percentile that corresponds to this score, and explain what that number represents.a) The probability that a score is from 185 to 210 is (Round to four decimal places as needed.)
The patient recovery time from a particular surgical procedure is normally distributed with a mean of 6.5 days and standard deviation of 1.3 days. Write your answers in percent form. Round your answers to the nearest tenth of a percent. a) What is the probability of spending less than 9 days in recovery? b) What is the probability of spending more than 7 days in recovery? c) What is the probability of spending between 7 days and 9 days in recovery?
3. The taxi and takeoff time for commercial jets is a random variable x with a mean of 8 minutes and a standard deviation of 3 minutes. Assume that the distribution of taxi and takeoff times is approximately normal. a). Find the probability that for 36 jets the average taxi and takeoff time is less than 8.33 minutes per plane. b). Find the probability that for 36 jets the average taxi and takeoff times is more than 8.55 minutes.
A survey was conducted to measure the height of Canadian men. In the survey, respondents were grouped by age. In the 20-29 age group, the height was normally distributed, with a mean of 69.2 inches and a standard deviation of 2.9 inches. A study participant is randomly selected. a) Find the probability that his height is less than 66 inches. b) Find the probability that his height is between 66 and 72 inches. c) Find the probability that his height is more than 72 inches. d) Find P10 , the 10th percentile please show all steps using excel formulas

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