Question

A random sample of college students majoring in cinematography were surveyed about their movie habits. One question inthe survey asked, "How many documentaries have you watched in the past month ?The table below represents theprobability density function for the random variable X, the number of documentaries watched by cinematography majors in the past month. Find the standard deviation of X.Round the final answer to two decimal places.

Answer 1

given the following data

x P(X=x) xP(x) (x - U)^2 . P(x)

4 1/5 4/5 (4 - 32/5)^2 . 1/5

6 2/5 12/5 (6 - 32/5)^2 . 2/5

8 2/5 16/5 (8 - 32/5)^2 . 2/5

U = 4/5 + 12/5 + 16/5 = 32/5

so,

= (4 - 6.4)^2 . 0.2 + (6 - 6.4)^2 . 0.4 + (8 - 6.4)^2 . 0.4

= (-2.4)^2 . 0.2 + (-0.4)^2 . 0.4 + (1.6)^2 . 0.4

= 5.76 x 0.2 + 0.16 x 0.4 + 2.56 x 0.4

= 1.152 + 0.064 + 1.024

= 2.24

therefore,

Standard Deviation (S.D)

S.D = square root of 2.24

S.D = 1.497

S.D = 1.50 (round to two decimal places)