Question

In: Statistics and Probability

Part 1: A particular telephone number is used to receive both voice calls and fax messages....

Part 1: A particular telephone number is used to receive both voice calls and fax messages. Suppose that 20% of the incoming calls involve fax messages, and consider a sample of 20 incoming calls. (Round your answers to three decimal places.)

(a) What is the probability that at most 6 of the calls involve a fax message?

(b) What is the probability that exactly 6 of the calls involve a fax message?

(c) What is the probability that at least 6 of the calls involve a fax message?

(d) What is the probability that more than 6 of the calls involve a fax message?


Part 2 : Suppose that 4% of the 2 million high school students who take the SAT each year receive special accommodations because of documented disabilities. Consider a random sample of 15 students who have recently taken the test. (Round your probabilities to three decimal places.)

(a) What is the probability that exactly 1 received a special accommodation?
(b) What is the probability that at least 1 received a special accommodation?
(c) What is the probability that at least 2 received a special accommodation?
(d) What is the probability that the number among the 15 who received a special accommodation is within 2 standard deviations of the number you would expect to be accommodated?
(e) Suppose that a student who does not receive a special accommodation is allowed 3 hours for the exam, whereas an accommodated student is allowed 4.5 hours. What would you expect the average time allowed the 15 selected students to be? (Round your answer to two decimal places.)

Part 3: An airport limousine can accommodate up to four passengers on any one trip. The company will accept a maximum of six reservations for a trip, and a passenger must have a reservation. From previous records, 45% of all those making reservations do not appear for the trip. Answer the following questions, assuming independence wherever appropriate. (Round your answers to three decimal places.)

(a) If six reservations are made, what is the expected number of available places when the limousine departs?
places

(b) Suppose the probability distribution of the number of reservations made is given in the accompanying table.

Number of reservations     3 4 5 6
Probability   0.09     0.19     0.29     0.43  

Let X denote the number of passengers on a randomly selected trip. Obtain the probability mass function of X.

x 0 1 2 3 4
p(x)                             

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Expert Solution

orchestra answered 1 year ago
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