In a certain population, it is given that 10% of the people weigh less than 41 kg and 30% of the people weigh more than the mean but less than 80 kg. (i) Assuming that the weights of the population are normally distributed, find the mean and standard deviation of the weights. Give your answer correct to three significant figures. (ii) Ten people are chosen at random. Find the probability that more than two of them weigh more than 80 kg. (iii) A committee consists of 120 people. Using a suitable approximation, find the probability that at most 18 of them weigh less than 41 kg. Show that your approximation is valid.
In a certain population, it is given that 10% of the people weigh less than 41 kg and 30% of the people weigh more than the mean but less than 80 kg. (i) Assuming that the weights of the population are normally distributed, find the mean and standard deviation of the weights. Give your answer correct to three significant figures. (ii) Ten people are chosen at random. Find the probability that more than two of them weigh more than 80 kg. (iii) A committee consists of 120 people. Using a suitable approximation, find the probability that at most 18 of them weigh less than 41 kg. Show that your approximation is valid.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:In a certain population, it is given that 10% of the people weigh less than 41 kg and 30% of the people weigh
more than the mean but less than 80 kg.
(i) Assuming that the weights of the population are normally distributed, find the mean and standard deviation
of the weights. Give your answer correct to three significant figures.
(ii) Ten people are chosen at random. Find the probability that more than two of them weigh more than 80 kg.
(iii) A committee consists of 120 people. Using a suitable approximation, find the probability that at most 18
of them weigh less than 41 kg. Show that your approximation is valid.
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