Question

Include examples if you can please.

1. How to use the z-value to calculate and interpret the area under a normal curve.

2.How to use the area under a normal curve to calculate the corresponding z-scores.

3.How to use the 68-95-99.7 Empirical rule-of-thumb to provide an estimate of a 68, 95 or 99.7 confidence interval for both means mu and proportions p.  

4.How to use the 68-95-99.7 Empirical rule-of-thumb to provide an estimate of the results of a test of hypotheses for both mu and p.

Answer 1

1)

Adult American male heights are on average 70 inches (5'10) with a standard deviation of 4 inches.

What is the probability that the average height of a group of 10 persons is between 65 and 75?

2)

Now suppose we have are under the curve. Suppose we have 10 people and we want to know what should the average height of 10 persons be so that their mean heights are in the lower 40% area of the curve, ie their mean height is in the lower 40% of the population.

So the average height should be lower of = 66.795 such that they will be in the lower 40% of the area.