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 median of the data set.

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

50	52	53	53
54	56	57	59
61	66	67	73

Answer 1

The data in ascending order is

50,52,53,53,54,56,57,59,61,66,67,73

Here we have 12 observations

n = 12

$mean = \frac{\sum x_i}{n} = \frac{701}{12} = 58.4167$

Standard deviation = 7.0641

Median will be an average of 6th and 7th observation = 56.5

So random variable is Z score of 56.5

$= \frac{56.5 - 58.4167}{7.0641}$

= -0.2713

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