Part 11) A sample of 50 observations is taken from a normal population, with µ=100 and o=10. If thepopulation is finite with N=250. Find:a) P(X > 103)b) P(98 < X < 101)c) Repeat above exercise with N=5002) The manufacture of cans of salmon that are supposed to have a net weight of 120g tells you thatthe 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 thestatement made by the manufacturer.3) The supervisor of a dairy milk chocolate factory has observed that the weight of each 32gchocolate bar is actually a normally distributed random variable, with a mean of 32.2g and astandard 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 fourbars will be less than 32g.c) Find the probability that, if a customer buys a pack of four bars, the mean weight of the fourbars will be greater than 32g.4) The manager of a restaurant in a commercial building has determined that the proportion ofcustomers who drink tea is 14%. What is the probability that in the next 100 customers at least10% will be tea drinkers?

As per our guidelines, we are allowed to answer first question only. Thanks 1) Given : μ = 100σ = 10…

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)

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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Estimation

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Question

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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