STAT 325 Attendance Check #6

Use the z-table to find the z-score for which the area to it's right is 0.2.

Answer explanation

A z-score with 0.2 to the right has 0.8 to the left. 0.8 is an area so find the area (the numbers in the middle of the table) closest to 0.8. Then, figure out which z-score that belongs to.

In this case, 0.8 is closest to 0.7995. 0.7995 is the area to the left of the z-score 0.84.

Find the z-scores that bound the middle 80% of the data (e.g. what z-scores have 80% of the data in between them?)

Answer explanation

If the middle has 80%, that means there must be 20% on the outside tails (so 10% in each tail. That means 10% must be to the left of the lower z-score, and 80% + 10% = 90% is to the left of the upper z-score.

Looking up the closest values to 0.1 and 0.9 in the middle of the table (middle because they are areas, not z-scores) end up in z-scores of -1.28 and 1.28 respectively.

Answer explanation

The mean of the sample mean is just the population mean μ, so in this case, 20.

Say that the mean length of all NFL football games is 3 hours with a standard deviation of 0.1. A random sample of 100 games is selected. What is the probability that the sample mean of this group is greater than 2.8 hours?

Answer explanation

Trying to find P(x-bar > 2.8):

First, turn 2.8 into a z-score: z = (2.8-3.0)/(0.1/sqrt(100)) = -2

Second, find P(Z > -2) using the z-table:

Looking up -2.00 in the z-table leads us to a probability of 0.0228. This is not the final answer though, this is P(Z < -2). We need to take 1 - 0.0228 = 0.9772.