Experience has shown that a grade in MAT 2371 is normally distributed with mean66 and variance 64 and that a grade in MAT 2377 is normally distributed with mean64 and variance 36. Suppose independence between the grades. Find theprobability that the class average in MAT 2371 will be higher than that in MAT 2377if there are 100 students in each of the courses. (No students are taking bothcourses.)0.02280.92070.57930.42070.9772

Answered: Image /qna-images/answer/61c82a67-70e9-4403-be59-2a893c6776d7.jpg

Answered: Experience has shown that a grade in…

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 hypothesis test was performed to decide whether the mean number of words spoken per day by men is fewer than for women. αα = 0.05 and p = 0.02. If a man and a woman are randomly selected there is a 2% chance that the man will speak fewer words than the woman on that day.
3 A play is enjoying a long run at a theatre. It is found that the play time may be modelled as a normal variable with mean 130 minutes and standard deviation 3 minutes, and that the length of the intermission in the middle of the performance may be modelled by a normal variable with mean 15 minutes and standard deviaton 5 minutes. Find the probability that the performance is completed in less than 140 minutes.
Suppose that X1, X2, X3 and X4 are all independent random variables, each with a normal distribution with mean 9 and variance 25. Define X-bar = (X1 + X2 + X3 + X4) / 4. Find Prob(X-bar > 10).
Last year, a person wrote 139 checks. Let the random variable x represent the number of checks he wrote in one day, and assume that it has a Poisson distribution. What is the mean number of checks written per day? What is the standard deviation? What is the variance? The mean number of checks written per day is (Round to three decimal places as needed.)
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Suppose that the miles-per-gallon rating of passenger cars is a normally distributed random variable with a mean and a standard deviation of 38.8 mpg and 4.1 mpg, respectively. What is the probability that a randomly selected passenger car gets at least 45 mpg? What is the probability that a randomly selected passenger car gets between 35 and 40 mpg? An automobile manufacturer wants to build a new passenger car with an mpg rating that improves upon 99% of existing cars. What is the minimum mpg that would achieve this goal?
From a large consignment of clementine fruit destined for a UK supermarket the cus- toms office is making a check at the boarder. According to the sender the weight of the fruit belongs to an unknown distribution of mean 50 g and variance 16 g. If the cus- toms officer takes 100 fruits at random what is the probability that their total weight will be more than 5040 g. Justify any assumptions you make in your calculations.
just subquestions 5 and 6 pleasee thank you so much!
The owner of a fast-food restaurant knows that, on average, 2.4 cars (customers) use the drive-through window between 3 pm and 3.15 pm. Find the variance and standard deviation Find the probability that exactly two cars will use the drive-through window Find the probability that at least three cars will use the drive-through window
A random variable has a longnormal distribution with mean 10 and variance 4. Calculate the probability that the variable will take a value between 7.5 and 12.5
Q3 A box contains 6 balls. Two are numbered 4, two are numbered 5, and two are numbered 6. The balls are mixed and one is selected at random. After a ball is selected, its number is recorded. Then it is replaced. If the experiment is repeated many times, find the variance (02) and standard deviation (o) of the numbers on the balls.
Rods are produced in large quantities in a factory. The masses of these rods are normally distributed with mean 250g and variance 9g. A random sample of 100 rods is selected. Find the probability that the mean mass of the rods in the sample will lie between 249g and 251g. If the rods are produced in batches of n and a batch is selected at random, find the least value of n such that the probability that the mean mass of the rods in the batch will lie between 249g and 251g is greater than 0.95.

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