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Part 1 1) A sample of 50 observations is taken from a normal population, with µ=100 and o=10. If the population is finite with N=250. Find: a) P(X > 103) b) P(98 < X < 101) c) Repeat above exercise with N=500

Part 1 1) A sample of 50 observations is taken from a normal population, with µ=100 and o=10. If the population is finite with N=250. Find: a) P(X > 103) b) P(98 < X < 101) c) Repeat above exercise with N=500

A First Course in Probability (10th Edition)
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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Part 1 1) A sample of 50 observations is taken from a normal population, with µ=100 and o=10. If the population is finite with N=250. Find: a) P(X > 103) b) P(98 < X < 101) c) Repeat above exercise with N=500 2) The manufacture of cans of salmon that are supposed to have a net weight of 120g tells you that the net weight is actually a random variable with a mean of 12lg and a standard deviation of 3.6g. Suppose that you take a random sample of 36 cans. a) Find the probability that the sample mean will be less than 119.4g. b) Suppose that you random sample of 36 cans produces a mean of 119g. Comments on the statement made by the manufacturer. 3) The supervisor of a dairy milk chocolate factory has observed that the weight of each 32g chocolate bar is actually a normally distributed random variable, with a mean of 32.2g and a standard deviation of 0.3g. a) Find the probability that if a customer buys ne chocolate bar, that bar will weigh less than 32g. b) Find the probability that, if a customer buys a pack of four bars, the mean weight of the four bars will be less than 32g. c) Find the probability that, if a customer buys a pack of four bars, the mean weight of the four bars will be greater than 32g. 4) The manager of a restaurant in a commercial building has determined that the proportion of customers who drink tea is 14%. What is the probability that in the next 100 customers at least 10% will be tea drinkers?
Transcribed Image Text:Part 1 1) A sample of 50 observations is taken from a normal population, with µ=100 and o=10. If the population is finite with N=250. Find: a) P(X > 103) b) P(98 < X < 101) c) Repeat above exercise with N=500 2) The manufacture of cans of salmon that are supposed to have a net weight of 120g tells you that the net weight is actually a random variable with a mean of 12lg and a standard deviation of 3.6g. Suppose that you take a random sample of 36 cans. a) Find the probability that the sample mean will be less than 119.4g. b) Suppose that you random sample of 36 cans produces a mean of 119g. Comments on the statement made by the manufacturer. 3) The supervisor of a dairy milk chocolate factory has observed that the weight of each 32g chocolate bar is actually a normally distributed random variable, with a mean of 32.2g and a standard deviation of 0.3g. a) Find the probability that if a customer buys ne chocolate bar, that bar will weigh less than 32g. b) Find the probability that, if a customer buys a pack of four bars, the mean weight of the four bars will be less than 32g. c) Find the probability that, if a customer buys a pack of four bars, the mean weight of the four bars will be greater than 32g. 4) The manager of a restaurant in a commercial building has determined that the proportion of customers who drink tea is 14%. What is the probability that in the next 100 customers at least 10% will be tea drinkers?
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