Question2: (Marks:7+3= 10) a) A random variable X has the following probabilityd

Question

Question2:                                                                                                                        (Marks:7+3= 10)

a)

A random variable X has the following probabilitydistribution:

x

4                            5                        6

P(x)

0.3                        0.5                      0.2

Find the mean and standard error of the mean for a randomsample of size 2.

b)

It is known that 3% of the persons living in Gujranwala city areknown to have a certain disease. Find the mean and standard errorof sampling distribution of proportion of diseased persons in arandom sample of 500 persons.

x

4                            5                        6

P(x)

0.3                        0.5                      0.2

Explanation / Answer

a) p = (4 x 0.3 + 5 x 0.5 + 6 x 0.2)/(4+5+6) = 0.3267 q = 1 - p = 0.6733 Mean = 2 x 0.3267 = 0.653 SE = SD/2 = (2 x 0.3267 x 0.6733)/2 =0.469 b) p = 0.03, q = 0.97 npq = (500 x 0.03 x 0.97) = 3.814 Mean = 500 x 0.03 = 15 SE = 3.814/500 = 0.171 Hope this helps!

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