Question

Problem 3.- An anthropologist wishes to estimate the average height of men for a certain race of people. i.- If the population standard deviation is assumed to be 2.5 inches and if she randomly samples 100 men, find an approximation to the probability that the difference between the sample mean and the true population mean will not exceed half an inch. ii.- Suppose that she wants the difference between the sample means and the popu- lation mean to be less than .4 inch, with probability .95. How many men should she sample to achieve this objective?

          Problem 3.- An anthropologist wishes to estimate the average height of men for a certain race of people.

i.- If the population standard deviation is assumed to be 2.5 inches and if she randomly samples 100 men, find an approximation to the probability that the difference between the sample mean and the true population mean will not exceed half an inch.

ii.- Suppose that she wants the difference between the sample means and the popu- lation mean to be less than .4 inch, with probability .95. How many men should she sample to achieve this objective?

Problem 3.- An anthropologist wishes to estimate the average height of men for a certain race of people.

i.- If the population standard deviation is assumed to be 2.5 inches and if she randomly samples 100 men, find an approximation to the probability that the difference between the sample mean and the true population mean will not exceed half an inch.

ii.- Suppose that she wants the difference between the sample means and the popu- lation mean to be less than .4 inch, with probability .95. How many men should she sample to achieve this objective?

Added by Jon W.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Shaiju T

04/30/2022

Step 1

So, in this case, it is 2.5/sqrt(100) = 0.25 inches. The difference between the sample mean and the population mean follows a normal distribution with mean 0 and standard deviation 0.25. We want to find the probability that this difference is less than 0.5 inches. Show more…

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Problem 3.- An anthropologist wishes to estimate the average height of men for a certain race of people. i.- If the population standard deviation is assumed to be 2.5 inches and if she randomly samples 100 men, find an approximation to the probability that the difference between the sample mean and the true population mean will not exceed half an inch. ii.- Suppose that she wants the difference between the sample means and the population mean to be less than .4 inch, with probability .95. How many men should she sample to achieve this objective?