*Using Chebyshev\'s Inequality* how many times must you toss a fair coin for there to be at least a 90% chance that the ratio of observed tails to total tosses will be between 0.4 and 0.6? Solution Chebyshev\'s inequality, P(|X-u|>k)>1- p^2/k^2 (p^2 is the variance)(u is the mean) So, P(u-k.

1. Using Computer Results. refer to the Minitab display in the margin. The probabilities were
obtained by entering the values of n = 6 and p = 0.723. There is a 0.723 probability that a
randomly selected American Airlines flight will arrive on time (based on data from the
Department of Transportation). In each case, assume that six and American Airlines flights are
randomly selected and find the indicated probability. Find the probability that at most two
American Airlines flights arrive on time. Is it unusual to have at most two of six American
Airlines flights arriving on time? Binomial with n = 6 and p = 0.723000
Solution
THis is the case of discrete random variable P(X<=2)=P(X=0)+P(X=1)+P(X=2)
=0.0005+0.0071+0.0462 =0.0538