11. Assume that the weights of individuals are independent and normally distributed with amean of 160 Ibs. and a standard deviation of 30 lbs. Suppose that 25 people squeezeinto an elevator that is designed to hold 4300 lbs. Determine the following:(a) The expected value and variance of the mean weight of the people.(b) Probability that the mean weight of the people is within 4 Ibs. of 160 lbs.(c) The probability that the load (the total weight) exceeds the design limit.(d) The design limit that is exceeded by 25 occupants with probability 0.0001.

Given Information: The eights of individuals are independent and normally distributed with a mean of…

Answered: 11. Assume that the weights of…

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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When a normal random variable Y is transformed to a standard normal random variable Z, the mean value of Z is 1 and the standard deviation value is 0.
A person's blood glucose level and diabetes are closely related. Let x be a random variable measured in milligrams of glucose per deciliter of blood. After a 12-hour fast, the random variable x will have a distribution that is approximately normal with μ = 85 and σ = 25. After 50 years of age, both the mean and standard deviation tend to increase. What is the probability that, for an adult under 50 years old, after a 12-hour fast, x is less than 130?
In 2008, the per capita consumption of soft drinks in Country A was reported to be 19.28 gallons. Assume that the per capita consumption of soft drinks in Country A is approximately normally distributed, with a mean of 19.28 gallons and a standard deviation of 4 gallons. Complete parts (a) through (d) below. a. What is the probability that someone in Country A consumed more than 15 gallons of soft drinks in 2008? The probability is
3. The mass of coffee in a randomly chosen jar sold by a certain company may be taken to have a normal distribution with means 203 g and standard deviation 2.5g. (i) Find the probability that a randomly selected jar will contain at least 200g of coffee. Obtain the probability that two randomly selected jars will together contain between 400g and 405g of coffee. (iii) The random variable ī denotes the mean mass (in grams) of coffee per jar in a random sample of 20 jars. Identify the value of a such that P(T – 203| < a) = 0.95. (ii)
A certain brand of automobile tire has a life expectancy that ie normally dietributed with a mean of u= 20000 milee and etandard deviation of o= 2500 milee. What ie the probability that a randomly chosen tire will last between 17500 miles and 25000 mileo? Select one: a. 0.8413 O b. 0.7 c. 0.8185 O d. 0.8
The level of nitrogen oxides (NOX) and nonmethane organic gas (NMOG) in the exhaust over the useful life (150,000150,000 miles of driving) of cars of a particular model varies Normally with mean 8080 mg/mi and standard deviation 66 mg/mi. A company has 1616 cars of this model in its fleet. Using Table A, find the level ?L such that the probability that the average NOX + NMOG level ?¯x¯ for the fleet greater than ?L is only 0.030.03 ? (Enter your answer rounded to three decimal places. If you are using CrunchIt, adjust the default precision under Preferences as necessary. See the instructional video on how to adjust precision settings.)
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
c. Vehicle speeds at a highway location have a normal distribution with mean u = 65 mph and standard deviation o = 5 mph. Find the probability that a randomly selected vehicle speed is greater than 73 mph.
The blood sugar levels of a person follows a normal curve with an average of 4.7mmol/L and a standard deviation of 1.4. In 2014, it is estimated that 8.5% of people around the world have diabetes. For the following questions: 1. Indicate whether the distribution to be used in answering the problem is a normal distribution 2. If yes, solve for the probability a. The probability of getting a random person with a high blood sugar level greater than 7mmol/L. b. The probability of getting a random sample of 150 people with less than 10% having diabetes c. The probability of getting a random sample of 60 people with less than 9% having diabetes d. The probability of getting a random sample of 150 people with a mean blood sugar level less than 5mmol/L. e. The probability of getting a random sample of 25 people with a mean of blood sugar level greater than 4.5mmol/L.
Women's heights are normally distributed with a mean given by u = 63.6 in. and a standard deviation given by o = 2.5 in. (a) If 1 woman is randomly selected, find the probability that her height is less than 62.6 in. Enter a number correct to 4 decimal places: (b) If 52 women are randomly selected, find the probability that they will have a mean height less than 62.6 in. Enter a number correct to 4 decimal places:
A person's blood glucose level and diabetes are closely related. Let x be a random variable measured in milligrams of glucose per deciliter of blood. After a 12-hour fast, the random variable x will have a distribution that is approximately normal with μ = 85 and σ = 25. After 50 years of age, both the mean and standard deviation tend to increase. What is the probability that, for an adult under 50 years old, after a 12-hour fast, x is more than 60?
I. NORMAL PROBABILITY DISTRIBUTION Cars are passing through a checkpoint. Assume the speeds are normally distributed such that the mean (u) = 61 mph and the standard deviation (sigma) = 4 mph. а. b. Calculate the probability (area under the curve) that the next car to pass will be travelling more than 58 mph.

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