Chapter 6.5

The Magazine Mass Marketing Company has received 14 entries in its latest sweepstakes. They know that the probability of receiving a magazine subscription order with an entry form is 0.6. What is the probability that more than 12 of the entry forms will include an order? Round your answer to four decimal places.

P(X>12)=P(X=13)+P(X=14) P(X=x)= nCx⋅p^x⋅(1-p)^n-x P(X=13) 14 C 13⋅(0.6)^13⋅(1−0.6)^14-13 =0.007314 14 C 14⋅(0.6)^14⋅(1−0.6)^14-14 =0.000784 0.007314+0.000784 =0.0081

Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. Round your answer to four decimal places. P(X>3), n=6, p=0.7

P(X>3)=1-[P(X=0)+P(X=1)+P(X=2)+P(X=3)] nCx⋅p^x⋅(1-p)^n-x 6 C 0⋅(0.7)^0⋅(1-0.7)^6-0 =0.000729 6 C 1⋅(0.7)^1⋅(1-0.7)^6-1 =0.010206 6 C 2⋅(0.7)^2⋅(1-0.7)^6-2 =0.059535 6 C 3⋅(0.7)^3⋅(1-0.7)^6-3 =0.18522 1-(0.000729+0.010206+0.059535+0.18522) 1-0.25569 =0.74431

Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. Round your answer to four decimal places. P(X≤4), n=6, p=0.8

P(X≤4)=P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4) nCx⋅p^x⋅(1-p)^n-x 6 C 0⋅(0.8)^0⋅(1-0.8)^6-0 =0.000064 6 C 1⋅(0.8)^1⋅(1-0.8)^6-1 =0.001536 6 C 2⋅(0.8)^2⋅(1-0.8)^6-2 =0.01536 6 C 3⋅(0.8)^3⋅(1-0.8)^6-3 =0.08192 6 C 4⋅(0.8)^4⋅(1-0.8)^6-4 =0.24576 0.000064+0.001536+0.01536+0.08192+0.24576 =0.34464

A real estate agent has 19 properties that she shows. She feels that there is a 30% chance of selling any one property during a week. The chance of selling any one property is independent of selling another property. Compute the probability of selling at least 5 properties in one week. Round your answer to four decimal places.

P(X≥5)=1−[P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)] P(X=x)= nCx⋅p^x⋅(1-p)^n-x 19 C 0⋅(0.3)^0⋅(1−0.3)^19-0 =0.001140 19 C 1⋅(0.3)^1⋅(1−0.3)^19-1 =0.009282 19 C 2⋅(0.3)^2⋅(1−0.3)^19-2 =0.035802 19 C 3⋅(0.3)^3⋅(1−0.3)^19-3 =0.086947 19 C 4⋅(0.3)^4⋅(1−0.3)^19-4 =0.149053 1-(0.00114+0.00928+0.03580+0.08695+0.14905) 1-0.282224 =0.7178

Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. Round your answer to four decimal places. P(X=14), n=16, p=0.8

nCx⋅p^x⋅(1-p)^n-x 16 C 14⋅(0.8)^14⋅(1-0.8)^16-14 =0.2111