Question

Let x be the binomial random variable with n=10 and p = 9 a. Find P(x = 8) and create a cumulative probability table for the distribution. b. Find P( x is less than or equal to 7) and P(x is greater than 7) c. Find the mean, u, the standard deviation, o, and the variance. d. Does the Empirical rule work on this distribution for data that is within one, two or three standard deviations of the mean? Explain. ante. Does Tchebysheff's theorem work on this distribution for data that is within 1, 1.5, 2 or 4 standard deviations of the mean? Explain.

Answer 1

n=10; p=0.9 ; 2=0,1 © FCX-8) - Ino.1)® Co.) --450.9) (0.1)= 0.1937 Cumulative distribution ma10; p=0,9 2 fea) pr*=) 0.0000 0.0000 2 0.0000. 3 0.0000 4 0.0001 5 0.0015 6 0.0112 7 0.0574 8 0.1937 q 0.3874 10 1.3487

PCX57) = 1-{P(x=f} +PC** 129) +P(X=10) = 1 -[1097%0,15+19, (09%0.5't 10, 10.9,"cars] = 0.0702 >(x77)- PODE) +POX 2) +PC*=lo) 0.9298 © mean ne = 1000.9)=9 vasarce = npa 1060.9)(0.1) -0.9 Standard deviation V npr 30.94868 -0.95 - Binomial distribution is different from: normal distribution Binomial distribution is discrete, not continuous Incase of sample size is larse onler, the shares can be similar . Binomial diftablution. Empirice rule cannot be applied to