deviation 3 and that random variable ? is normal with mean 0 and standard deviation 4. Suppose that ? and ? are independent, use an appropriate method to determine his probability distribution of the random variable ? + ?.

deviation 3 and that random variable ? is normal with mean 0 and standard deviation 4. Suppose that ? and ? are independent, use an appropriate method to determine his probability distribution of the random variable ? + ?.

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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2.2) The average price of cell phones manufactured by Ahmadi, Inc. is $100 with a standard deviation of $10. Furthermore, it is known that the prices of the cell phones manufactured by Ahmadi are normally distributed. a) Suppose cell phones manufactured by Ahmadi, Inc. are used in a test. Find the probability that exactly two of the three cell phones have prices less than $100.
3. 3c. A. B. Women have head circumferences that are normally distributed with a mean of 23.55 inches and a standard deviation of 0.93 inches. If the HATS BY CHARLIE company produced hats so that they fit head circumferences between 22.2 inches and 24.2 inches, then what is the probability that a woman can fit into these hats? A. If the HATS BY CHARLIE company produced hats so that they fit head circumferences between 22.2 inches and 24.2 inches, then what is the probability that a randomly selected group of 40 woman can fit into these hats? B. Write a sentence or two that explains your answer to 3B and why you think that answer is correct in connection to your answer in 3A.
The state of California has a mean annual rainfall of 19 inches, whereas the state of New York has a mean annual rainfall of 48 inches (Current Results website, October 27, 2012). Assume that the standard deviation for both states is 4 inches. A sample of 30 years of rainfall for California and a sample of 45 years of rainfall for New York has been taken. a. Show the probability distribution of the sample mean annual rainfall for California. This is a normal probability distribution with and (to decimals). b. What is the probability that the sample mean is within inch of the population mean for California? (to decimals) c. What is the probability that the sample mean is within inch of the population mean for New York? (to decimals) d. In which case, part (b) or part (c), is the probability of obtaining a sample mean within inch of the population mean greater? Why? The probability of being within inch is greater because the sample size is .
Two devices are used to measure the length of beam. If the true length of the beam is L, the measurement error made by one device, E, , is normally distributed with mean 0 and standard deviation 0.006L, and the measurement error made by the other device, E, , is normally distributed with mean 0 and standard deviation 0.004L. The two measurement errors are independent of each other. What is the probability that the average value of the two measurements, (E, + E,)/2, is within 0.5% of L? Note that this problem can be done using the attached table of the cdf of the standard normal random variable.
2. Suppose X is a normally distributed random variable with a mean of 9.00. If the probability that X is less than 9.66 is 0.67, then what is the standard deviation of X?
Suppose that the grades of Mathematics module is modeled well by a normal probability distribution with mean (170) and standard deviation (220). Let X be the random variable representing this distribution. Find two symmetric values “a” and “b” such that ??????????? [ a < ? < ? ] = 0.99 , where ?=−?
Suppose the demand for a company’s product in week 1,2, & 3 are each normally distributed. The means are 50, 45, and 65. The standard deviations are 10,5, and 15. Assume these 3 demands are probabilistically independent. Suppose the company has 180 units in stock, and it will not be receiving any more shipments from its supplier for at least 3 weeks. What is the probability that stock will run out during the 3 week period? How many units should the company have in stock, so that it can be 98% certain of not running out during the 3 week period , assuming it will not receive any more shipments during this period?
The 3-point shooter star of your favourite team usually attempts six 3-point shots in a basketball game. The team record shows that the shooter makes 25% of all 3-point shots attempted in a game. Assuming that the shots are independent of each other,what is probability that the star will make shots at least 1.25 standard deviation more than the expected?
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.
The weights of large eggs are normally distributed with mean 65 grams and standard deviation 4 grams. The weights of standard eggs are normally distributed with mean 50 grams and standard deviation 3 grams. 1. One large egg and one standard egg are chosen at random. Find the probability that the weight of the standard egg is more than 4/5 of the weight of the large egg. 2. Standard eggs are sold in packs of 12 while large eggs are sold in packs of 5. Find the probability that the weight of a pack of standard eggs differs from twice the weight of a pack of large eggs by at most 5 grams. This is Probability and Statistics