The distribution of heights of adult males has a mean of 69 inches and a standard deviation of 4 inches. A random sample of 36 adult males is selected. Find the probability that the average height will be more than 70 inches.

a. 0.668
b. 0.858
c. 0.908
d. 0.995

And for this case we can use the complement rule and the normal standard distribution of excel and we got:

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:

Where and

And we select a sample size of n =70

From the central limit theorem  (n>30)we know that the distribution for the sample mean is given by:

And we want to find this probability:

And we can use the z score formula given by:

And using this formula we got:

And for this case we can use the complement rule and the normal standard distribution of excel and we got:

.24

step-by-step explanation:

the probability is   .24

the first player had the highest probability of getting a silver marble

the game could be made fair by adding back the marble that was drawn after each draw