Question

) 6. Let x be the binomial random variable with n = 10 and p = .9

            (2) a. Find P(x = 8)     

            (5) b. Create a cumulative probability table for the distribution.

            (2) c. Find P( x is less than or equal to 7)   

      

            (2) d. Find P(x is greater than 7)

1. e. Find the mean, μ.    

  

            (1) f. Find the standard deviation, σ.

           

            (1) g. Find the variance.

                                                                                                                                     

            (3) h. Does the Empirical rule work on this distribution for data that is within one, two or three standard deviations of the mean? Explain.

            (3) i. 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.

I am confused about what is in bold.

Answer 1

Solution Xo Binomial (= 10, P=0.9) X=0,1, -..., 10 P(x-3) - (0) (0.9)*(1-02)lo. 2 10-8 (a) now Px3 6) : co (0.9)8 (1-0.9) 0.1571 table cummulative probability 8 G S oto 3 4 sle 1 2 0 0 0.002 0.0130.070 0.624 0 0 P(x22) 10 I 닛 PCX2x) 0.651 1- P(x77) (c) P(x<) ) 11.(p(x=8) + P(x=9) + P(x a to)] 0.070 table pixs 7) = asove OCO froam

(d) P(x>) l-PCX57) 1-0.070 0.93 (e) (x)=da Opa 1ox0.95 9 (f) Standard devication Jop (e-p) lox0.9 (1-0.9) 0.949 (9) op 10.94912. 0.9 vaince 15