X is a random variable with mean 10 and variance 10 Use Ch

X is a random variable with mean = 10 and variance = 10. Use Chebyshey\'s inequality to determine an interval for X, such that the probability is at least 0.9 that times is in that interval.

Solution

We need to find the amount of standard deviations that will have at least 90% of data

Thus,

1 - (1/k)² = 0.90

Thus,

k = sqrt( 1 / 0.1)

= sqrt ( 10)

= 3.16 Standard devaitions from the mean

Thus,

confidence interval = 10 +/- k(sqrt(10)

thus, the confidence interval = 10 +/- (sqrt(10) * sqrt(10)

= 10 +/- 10

= (0 , 20)

Hope this helps.