The average sales price of a home in Ourtown U.S.A. is $120,000.

The population standard deviation is $20,000. 

What is the probability that the next home will sell for more than $130,000?

We are trying to determine the average age of the Cardinal baseball fan. We know that the age distribution of Cardinal nation is normally distributed with a standard deviation of 20. We need to determine the average age. We take a sample of 40 fans and the average of our sample is 42 years old. 

What is the 95% confidence interval (range) for our sample average of 42? (remember – confidence intervals are always 2- tailed (plus or minus)).

We are trying to determine the average age of the Cardinal baseball fan. We know that the age distribution of Cardinal nation is normally distributed with a standard deviation of 20. We need to determine the average age. We take a sample of 40 fans and the average of our sample is 42 years old. 

However, the Cardinal President of Operations wants a 98% confidence interval of plus or minus 5.0. What sample size do we need to satisfy his request?

The Cardinals average 4 extra inning games per month. 

What is the probability that they will have more than 4 extra inning games next month? Hint – Poisson distribution.

A real estate tycoon wants to test the hypothesis that the percentage of people who own their own home in Florida is the same as the home ownership percentage in Georgia. He states his null hypothesis as 'the Florida percentage is the same as the Georgia percentage' and the alternative hypothesis is 'the percentages are significantly different'. He decides on a 2-tailed test and he samples 400 Florida homes and 600 Georgia homes. His sample results:

Florida - 280 homeowners out of 400 (.7)

Georgia - 384 homeowners out of 600 (.64)

a percentage difference of .06

What is the lowest confidence percentage that will support his rejection of the null hypothesis? Stated another way – what is the highest percentage that will support his acceptance of the null hypothesis?

The average age of our customers is 40 years with a standard deviation of 10 years. 

What is the probability that the next customer to enter our store will be between 30 and 50 years old ?

The Z Table is the cornerstone of intro stats. It translates the 'number of standard deviations from the mean' into a percentile (.90, .95. .99. etc.). The table is laid out with the assumption that the test being conducted is a 'one-way' test, meaning that the Z value is greater than some percentile (if Z is positive) or less than some percentile (if Z is negative). Another way of saying this is: the Z table only measures the area under the curve for 1 of the 'tails' (either the extreme right or the extreme left). So, if we have a 2 tailed test for say 95% confidence, then we must put 2.5% in our right tail and 2.5% in our left tail. Conversely, a one tailed test for 95% puts 5% in the right tail only. 

Arrange the 5 following confidence intervals in ascending (lowest to highest) order of their Z value:

A) 2 tailed test at 95%

B) 1 tailed test at 95%

C) 1 tailed test at 90%

D) 2 tailed test at 99%

E) 1 tailed test at 99%

Ben is given a simple stats problem. Of the 1,000 students at Our Town Community College, 600 are female, 400 are male. The problem asks: if we select 20 students at random, what is the probability that our sample of 20 will contain 10 or 11 or 12 or 13 females. 

The simple solution is to go to the binomial table and add up the 4 probabilities of 10, 11, 12 and 13 with a population percentage of 0.6: 

However, Ben likes to do things the hard way. He decides to use the normal distribution as an approximation to the binomial. Why? No one knows why. Ben is just Ben. 

He gets the Z value and percentile for 9.5 and then obtains the Z value and percentil value for 13.5. He then subtracts the 9.5 percentile from the 13.5 percentile and hopefully ends up with something close to .6224

What is:

the Z value for 9.5 

the percentile for 9.5  

the Z value for 13.5 

the percentile for 13.5 

We randomly sampled 175 people in Our Town USA and found that 62.9% of them favored Coke over Pepsi. We decided on a 90% 2 tailed test (z=1.64) and proclaimed that we were 90% confident of the 62.9% plus or minus 6%. 

We arrived at the 6% by first calculating the standard deviation:

and then multiplying .0365 by z (1.64)

What sample size do we need to be plus or minus 4%?

A data set comprises a large number of entries. What is the interquartile range of the set?

Statement 1: The 75th percentile is 745

Statement 2: The median is 556