Question

6) An official from the securities commission estimates that 70% of all online bankers have profited from the use of insider information. Assume that 15 online bankers are selected at random from the commission's registry. What is the probability that exactly 8 have not profited from insider information? What is the probability that at most 5 have profited from insider information? What is the probability that not all the selected online bankers have profited from insider information? What is the probability that more than 12 have profited from insider information? How many of the 15 online bankers would you expect to have profited from insider information? Use the binomial formula and round it to 4 decimal.

Answer 1

Given p = 0.70 and number of trials n = 15

We will TI 84 function binomcdf(n,p,k) and binompdf(n,p,k)

(A) P(X=8) = binompdf(n,p,k)

setting n=15, p(not profit) =1- 0.7 = 0.3 and k =8

P(X=8) = binompdf(15,0.3,8) = 0.0348

(B) P(X at most 5) = binomcdf(n,p,k)

setting n=15, p(profit) = 0.7 and k =5

P(X at most 5) = binomcdf(15,0.7,5) = 0.0037

(C) P(X not 15) = 1 - binompdf(n,p,k-1)

setting n=15, p(profit) = 0.7 and k =15

P(X not 15) =1- binompdf(15,07,15-1) = 0.9953

(D) P(X >12) = 1- binomcdf(n,p,k)

setting n=15, p(profit) = 0.7 and k =12

P(X >12) =1- binomcdf(15,0.7,12) = 0.1268

(E) Expected value = n*p

setting n = 15 and p = 0.7

we get

E[x] = 15*0.7 = 10.5