Question

A set of sample data has a mean of 81 and a standard deviation of 6. Approximately what percentage of the data is between 75 and 87?

Answer 1

we can fit all normal distributions of varying means and sds into a standard normal distribution by first shifting it to a mean of 0 and dividing out the sd so the sd=1

Answer 2

that means all points get shifted along with it:

(75-81) and (87-81)

we divide out the sd of 6; since 6/6 = 1

(75-81)/6 and (87-81)/6

and this gives us values that we can measure against

Answer 3

the zscore produced tells us how many sds away from the mean we are. and depending on how far away we are, we can determine how much of the data will fit in between our given points

Answer 4

the math says; we are 1 sd to the left; and 1 sd to the right of the mean; whcih is about 68% of the data entotal