Assume the random variable X has a binomial distribution with the given probabil
ID: 3053067 • Letter: A
Question
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?2), n=6, p=0.2
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=15), n=18, p=0.8
A researcher wishes to conduct a study of the color preferences of new car buyers. Suppose that 40% of this population prefers the color red. If 15 buyers are randomly selected, what is the probability that exactly two-fifths of the buyers would prefer red? Round your answer to four decimal places.
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 0.5. What is the probability that less than 10 of the entry forms will include an order? Round your answer to four decimal places.
A real estate agent has 17 properties that she shows. She feels that there is a 40% 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 no more than 3 properties in one week. Round your answer to four decimal places.
Explanation / Answer
Question 1 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?2), n=6, p=0.2
Answer : P(X > =2) = 1 - [6C0 (0.2)0(0.8)6 + 6C1 (0.2)1(0.8)5] = 1- 0.6554 = 0.3446
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=15), n=18, p=0.8
Answer : P( X = 18) = 18C15 (0.8)15(0.2)3 = 0.2297
A researcher wishes to conduct a study of the color preferences of new car buyers. Suppose that 40% of this population prefers the color red. If 15 buyers are randomly selected, what is the probability that exactly two-fifths of the buyers would prefer red? Round your answer to four decimal places.
Answer : Pr(Prefers color red) = 0.40
Sample size n = 15
Pr(Exactly two fifth of the buyers prefer red) = Pr(X = 6 ; 15; 0.4) = 15C6 (0.4)6(0.6)9 = 0.2066
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 0.5. What is the probability that less than 10 of the entry forms will include an order? Round your answer to four decimal places.
Answer : Sample size = 14
Pr(Megazine subscription) = 0.5
Pr(X < 10) = BIN(x < 10 ; 14 ; 0.50) = 0.9102
A real estate agent has 17 properties that she shows. She feels that there is a 40% 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 no more than 3 properties in one week. Round your answer to four decimal places.
Answer : Pr(elling a prporty) = 0.40
Pr(x <= 3) = Pr(x < = 3 ; 17 ; 0.40) = 0.0464
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