intro to stats help!!!

Question

A random experiment involves drawing a sample of 12 data values from a normally distributed population. The random variable is the z-score of the minimum of the data set.

30	32	37	44
45	47	47	48
56	57	58	67

Give the random variable. (Appropriate rounding rules still apply.)

r.v. =

Answer 1

The equation for z-score requires the mean (μ) and standard deviation (σ). So first calculate those.

You can use a calculator such as a TI-84 to do that. Enter the numbers in a list and then, for the TI-84, use the button "stat", scroll to "CALC", then "1:1-Var Stats"

The mean is 47.333333 and the standard deviation (use Sx) is 10.99035

The minimum of the data set is 30. So the z-score is (30 - 47.333333)/10.99035 = -1.5771 (I'm unsure what your "appropriate rules for rounding are).

Answer 2

47 = the mode and median

mean = 47 1/3 which has z score = 0

calculate standard deviation = sd

z score for 30 = (30-47 1/3)/sd= -(17 1/3)/sd

sd = sqr of (sum of squared differences from the mean divided by 11)

you'd divide by 12 if the data were the entire population

but divide by 12-1 = 11 since it is a sample

sd = about 10.99

z score for minimum 30 = (-52/3)/10.99

z = about -1.58

any value < mean will have a negative z score