In this chapter we will consider two very specific random variables where the random event that produces them will be selecting a random sample and analyzing it.

Now get another sample of size n and compute for that sample.. Do this again, and again, and again… until every possible sample of size n has been collected and for each has been calculated.

Suppose samples of size n are chosen from a population where the population proportion of success is p. Then: The values of approximately follow a normal distribution if both ; that is, the sample size is large enough that we would expect to see at least 10 “Y” and at least 10 “N”

The manager at a certain company believes that 2% of the batteries made at his factory are defective. (a) Would collecting samples of size 250 generate a distribution of that is approximately normal? (b) Would collecting samples of size 1000 generate a distribution of that is approximately normal? (c) What are the mean and standard deviation of the distribution for samples of size n = 1000?

The manager at a certain company believes that 2% of the batteries made at his factory are defective. (d) What is the probability that in a random sample of 1000 such batteries, between 1.4% and 1.8% are defective? (e) What is the probability that in such a sample, less than 1% are defective? (f) What is the probability that in such a sample, more than 3.5% are defective?

Imagine taking a sample of size n from some population, measuring some specific numerical variable for each and then finding the average value for that sample, For example: get a sample of 40 XU students, measure their height, and then calculate the average height of the sample.

Now get another sample of size n and calculate for it. Now get another sample, and another, and another… We now have a numerical data set consisting of many observations of values of ; this data set has a mean, it has a standard deviation, and its histogram has a shape (center, shape, and spread).

Suppose samples of size n are chosen from a population having population mean μ and standard deviation σ. Then: If the population is normal or if the sample size is sufficiently large, the distribution of is approximately normal.

A certain brand of light bulb advertises an average life span of 1400 hours with a standard deviation of 42.5 hours. (a) What is the probability that in a random sample of 64 of these light bulbs the average lifespan is between 1385 hours and 1395 hours? (b) What is the probability that in a random sample of 100 of these light bulbs the average life span is less than 1390 hours?

A certain brand of light bulb advertises an average life span of 1400 hours with a standard deviation of 42.5 hours. (c) What is the probability that in a random sample of 225 of these light bulbs the average life span is more than 1410 hours? (d) What values make up the top 2% of all average lifespans for samples of size 500 of these light bulbs?