1. Full-time Ph.D. students receive an average of P12837 per year. If the averagesalaries are normally distributed with a standard deviation of P1500, find theseprobabilities: (a) the student makes more than P15,000; (b) the student makesless than P12,000; (c) if there are 250 full-time Ph.D. students, how manystudents make more than P15,000? *

Answered: Image /qna-images/answer/32555525-36af-4be3-8cfb-31f118628715.jpg

Answered: 1. Full-time Ph.D. students receive an…

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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Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find the probability of obtaining a reading between -0.51°C and -0.47°C.
Suppose that, on average, electricians earn approximately µ = $54,000 per year in the United States. Assume that the distribution for electricians’ yearly earnings is normally distributed and that the standard deviation is σ = $12,000. What is the probability that the average salary of four randomly selected electricians exceeds $60,000?
Research scientists report that mice will live an average of 40 months with a standard deviation of 3 months when their diets are sharply restricted and then enriched with vitamins and proteins. A. Estimate the probability that a given mouse will live between 31 and 49 months if the distribution is unknown.B. Calculate the same probability if the lifetimes of such mice are normally distributed.
Assume that IQ scores of Red Sox are normally distributed with a mean of 63.6 and a standard deviation of 2.5. if 90 Red Sox are randomly selected, find the probability that they have mean IQ score between 62.9 and 64.0
The state of California has a mean annual rainfall of 22 inches, whereas the state of New York has a mean annual rainfall of 42 inches. Assume that the standard deviation for both states is 4 inches. A sample of 31 years of rainfall for California and a sample of 49 years of rainfall for New York has been taken. (a) Show the probability distribution of the sample mean annual rainfall for California. -2.1-14-0.7 0 0.7 1.4 2.1 199 200 21.3 22 22.7 234 24.1 inches inches ^^ inches 39.9 40.6 41.3 42 42.7 434 44.1 @0 10 14 18 22 26 (b) What is the probability that the sample mean is within 1 inch of the population mean for California? (Round your answer to four decimal places.) (c) What is the probability that the sample mean is within 1 inch of the population mean for New York? (Round your answer to four decimal places) (a) In which case, part (b) or part (c), is the probability of obtaining a sample mean within 1 inch of the population mean greater? Why? 30 34 inches
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 the average age of a Tulane undergraduate is 20 years with a standard deviation of 1.2 years. Suppose we obtain a random sample of 80 tulane undergraduates. Find the probability that the sample average is at least 20.3 years.
The maternity ward at a certain hospital in a certain country in Africa is one of the busiest in the world with an average of 60 births per day. Let X= the number of births in an hour. Find the mean and standard deviation of X. What is the probability that the maternity ward will deliver three babies in one hour? What is the probability that the maternity ward will deliver at most three babies in one hour? What is the probability that the maternity ward will deliver more than five babies in one hour?
A professor knows that her statistics students' final exam scores have a mean of 79 and a standard deviation of 12.4. In his class, an "A" is any exam score of 90 or higher. This quarter she has 25 students in her class. What is the probability that 7 students or more will score an "A" on the final exam?
Q. 3 In a large population of adults, 45% have a University degree. If people are selected at random from this population: (i) Find the probability that the third person selected is the first one that has a post University degree. (ii) Find mean and standard deviation of this geometric distribution.
A population of values has a mean of 233.8 and standard deviation of 44.4. Find the probability that a sample of 46 values from this population will have a mean between 234.5 and 245.6.
Suppose that a brand of lightbulb lasts on average 1690 hours with a standard deviation of 194 hours. Assume the life of the lightbulb is normally distributed. Calculate the probability that a particular bulb will last from 1418 to 2183 hours?

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