(R) The Distribution of Sample Means

Below are two examples which illustrate a statistical concept:

The Distribution of Sample Means:

The average mortgage for new families in Texas in $ 1300, with a standard deviation of $ 800. If 100 new families are surveyed, what is the probability that the mean mortgage payment will exceed $ 1500?

800/sqrt(100)

[1] 80

(1500-1300) / 80

[1] 2.5

pnorm(2.5, lower.tail=FALSE)

[1] 0.006209665

There is a 0.62% chance of this occurring.

An American football team typically scores 17 points per game, with a standard deviation of 3 points. In a sample of 16 games, what is the probability that the team scored an average of between 16 - 19 points?

3/sqrt(16)

[1] 0.75

(16 - 19) / 0.75

[1] -4

1 - pnorm(-4, lower.tail = TRUE) * 2

[1] 0.9999367

There is a 99.99% chance of this occurring.