**Text Transcription for Educational Website:**---**Problem Statement:**Suppose that Wall A is constructed by stacking 30 metal blocks, and that the height of each metal block is an independent $ \mathcal{N}(50, 10) $ normal random variable. Suppose that Wall B is constructed by stacking 25 wood blocks, and that the height of each wood block is an independent $ \mathcal{N}(61, 4) $ normal random variable.(a) What are the distributions of the heights of Wall A and Wall B?(b) What is the probability that Wall A is taller than Wall B?---The text poses a statistical problem involving the construction of two walls, where Wall A consists of metal blocks and Wall B consists of wood blocks. The problem requires determining the probability distributions of the heights of the two walls and then finding the probability that Wall A is taller than Wall B.

Answered: Suppose that Wall A is constructed by…

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 manager of a restaurant believes that waiters and waitresses who introduce themselves by telling customers their names will get larger tips than those who don't. In fact, she claims that the average tip for the former group is 16% while that of the latter is only 12%. If tips are normally distributed with a standard deviation of 8%, what is the probability that in a random sample of 15 tips recorded from waiters and waitresses who introduce themselves and 15 tips from waiters and waitresses who don't, the mean of the former will exceed that of the latter? Probability= 16.75
The taxi and takeoff time for commercial jets is a random variable x with a mean of 8.4 minutes and a standard deviation of 3.3 minutes. Assume that the distribution of taxi and takeoff times is approximately normal. You may assume that the jets are lined up on a runway so that one taxies and takes off immediately after the other, and that they take off one at a time on a given runway. (a) What is the probability that for 38 jets on a given runway, total taxi and takeoff time will be less than 320 minutes? (Round your answer to four decimal places.)(b) What is the probability that for 38 jets on a given runway, total taxi and takeoff time will be more than 275 minutes? (Round your answer to four decimal places.)(c) What is the probability that for 38 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes? (Round your answer to four decimal places.)
The results of a study showed that heterosexual women, during ovulation, were significantly better at correctly identifying the marriage status of a man from a photograph of his face than women who were not ovulating. Near ovulation, on average women correctly identified the marriage status of about 67% of the 100 men shown to them. Assume that the sample distribution for this study is unimodal and symmetric and that the samples are collected randomly. If this is the probability of correctly identifying the marriage status of a man in any given photograph, what is the probability a woman would correctly classify 79 or more of the men? What is the probability?
The taxi and takeoff time for commercial jets is a random variable x with a mean of 9 minutes and a standard deviation of 3.4 minutes. Assume that the distribution of taxi and takeoff times is approximately normal. You may assume that the jets are lined up on a runway so that one taxies and takes off immediately after the other, and that they take off one at a time on a given runway. (a) What is the probability that for 35 jets on a given runway, total taxi and takeoff time will be less than 320 minutes? (Round your answer to four decimal places.) (b) What is the probability that for 35 jets on a given runway, total taxi and takeoff time will be more than 275 minutes? (Round your answer to four decimal places.) (c) What is the probability that for 35 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes? (Round your answer to four decimal places.) US 12:44 hp DII -> & $ @ 7 8 3. 4 5 i y r W k d m V .. ..
My bus is scheduled to depart at noon. However, we're in Randomland, and this means the departure time varies randomly with average departure time 12 o'clock and a standard deviation of 6 minutes. Assume the departure time is normally distributed. If I get to the bus stop 5 minutes past noon, what is the probability that the bus has not yet departed?
A company is introducing a new product. It has 100 retail locations each independently agreeing to offer it with probability 0.2. The amount of sales of the new product in each location is a normal random variable with average 100 and standard deviation 15. Calculate the expectation of the total sales of the new product. Calculate the variance of the total sales of the new product.
I asked this question before, and got an answer, but I have a question about the response that was given. The original question was: For an initial investment of 100, an investment yields returns of X1 and X2, where X1 and X2 are independent normal random variables with mean 60 and variance 25. What is the probability that the rate of return of this investment is greater than 10%? In the answer that was given it says that the gain of the investment is X1+X2. My question is why can we just group those together as one amount? I was given a formula in my class that says the return on the investment would be the solution to the equation: -100+ X1/(1+r) + X2/(1+r)2=0. If this formula is used, a different solution would result for this problem.
One common disease among pediatric patients is streptococcal pharyngitis (strep throat). If a pediatric patient comes in to the pediatricians feeling ill, there is a 26% chance that they have strep throat. A doctor sees 7 pediatric patients on a particular day (assume these patients are independent). Consider the random variable is a binomial random variable such that X = number of pediatric patients with strep throat. What is the expected number of pediatric patients with strep throat?
Assume IQ’s of adults in a certain country are normally distributed with mean 100 and SD 15. Suppose a president, vice president, and secretary of state are chosen randomly from the adults in the country, with each adult having an equal chance to be assigned each of the 3 jobs. What is the probability that the president will have an IQ of at least 107.5 and that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130?
The taxi and takeoff time for commercial jets is a random variable x with a mean of 8.7 minutes and a standard deviation of 3.5 minutes. Assume that the distribution of taxi and takeoff times is approximately normal. You may assume that the jets are lined up on a runway so that one taxies and takes off immediately after the other, and that they take off one at a time on a given runway. (a) What is the probability that for 33 jets on a given runway, total taxi and takeoff time will be less than 320 minutes? (Round your answer to four decimal places.)(b) What is the probability that for 33 jets on a given runway, total taxi and takeoff time will be more than 275 minutes? (Round your answer to four decimal places.)(c) What is the probability that for 33 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes? (Round your answer to four decimal places.)

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