Question

When a randomly selected number A is rounded off to its nearest integer RA , it is reasonable to assume that the round-off error A−RA is uniformly distributed in (−0.5, 0.5). If 50 numbers are rounded off to the nearest integer and then averaged, approximate the probability that the resulting average differs from the exact average of the 50 numbers by more than 0.1.

Answer 1

Answer:

giventhat

n = 50,

X = differnce in resulting average from exact average)

As the round off error A_RA is uniformly distributed in (-0.5,0.5)

mean of X = 0

variance of X is (b-a)2 / 12 ,here b = 0.5 ,a = -0.5

variance = 1/12 ,sd = 0.2886

hence Z = (X -0 )/ 0.2886 follows standard normal distribution.

P(|X|>0.1)

= 1 - P(-0.1 < X <0.1)

= 1 - P(-0.1*3.4641 <Z < 0.1*3.4641)

1 - P( -0.34641<Z<0.346641)

= 1 - 2(0.6331-0.5) = 2 - 1.2662 = 0.7338

variance