Normally distribution

Question

A pharmaceutical company makes tranquilizers. It is assumed that the distribution for the length of time they last is approximately normal. Researchers in a hospital used the drug on a random sample of 9 patients. The effective period of the tranquilizer for each patient (in hours) was as follows: 2.5; 2.8; 3.0; 2.3; 2.3; 2.2; 2.8; 2.1; and 2.4.

NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

(i)    x = 

 (rounded to two decimal places)

(ii)    s_x = 

 (rounded to two decimal places)

(iii)    n = 

(iv)    n − 1 =

Answer 1

x = mean = arithmetic average = sum of all 9 divided by 9 = 2.4888... = about 2.49

s = square root of variance,

s^2 = variance = sum of squared differences from the mean all divided by 8, very tedious calculations. if it were the population and not a sample, divide by 9

s= about 0.31

'

n = 9

n-1 = 8