Question

QUESTION 4

1. You are provided with the following data regarding number of hours slept last night:

   5

   6

   2

   4

   8

   9

   2

   7

   3

   8

   4

   What is the value of 'n'?

   What is the mean?

   What is the standard deviation?

   What is the z-score for 6?

   What proportion of our population would be expected to sleep between 4 and 8 hours?

   ROUND Z-SCORES TO TWO DECIMALS. ROUND ALL OTHER CALCULATIONS TO FOUR DECIMALS.

Answer 1

There are 11 values hence n = 11.

mean = sum of values / n = (5+6+2+4+8+9+2+7+3+8+4)/11 = 5.2727

Standard deviation is given by s =  

= sqrt[ {(5-5.27)^2 + (6-5.27)^2 + ....... + (4-5.27)^2 } / 11-1] = 2.4936

z score = X - mean / s

z score = (6-5.27)/2.49 = 0.293 ~ 0.29

P(4 < X < 8) = P( (4-5.27)/2.49 < Z < (8-5.27)/2.49 ) = P( -0.51 < Z < 1.096)

which from standard normal distribution table comes out to be 0.86346 - 0.30503 = 0.55843 ~ 0.5584