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The College Board reports that 2% of the two million high school students who take the SAT each year receive special accommodations because of documented disabilities (Los Angeles Times, July 16, 2002). Consider a random sample of 25 students who have recently taken the test.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 25 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 h for the exam, whereas an accommodated student is allowed 4.5 h.

Respuesta :

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Answer:

a.) 0.0379

b.) 0.3965

c.) 0.0886

d.) 0.7

Step-by-step explanation:

Data

Let P = P(student receives special accommodation)

        = 0.02

then X = number among 25 who ahve recieved a special accommodation

Then X ≈ Bin (25, 0.02)

a.) Probability that 1 candidate received special accommodation

P(X = 1) =  (25 1) ([tex](0.02^{1} )(1-0.02)^{25-1} = 25(0.02)(0.98)^{24}[/tex] ≈ 0.3079

b.) probability that at least 1 received a special accommodation is given by:

P(X≥1) = [tex]1 - P (X = 0) = 1 - ( 25 0) (0.02)^{0} (1-0.02)^{25} = 1 - (0.98)^{25}[/tex]

                                                                                    ≈ 1 - 0.6035

                                                                                    = 0.3965

c.) probability that at least 2 received a special accommodation is given by:

P (X≥2) = 1 -P(X=0) - P(X=1)

            ≈ 1 - 0.6035-0.3079

             = 0.0886

d.) Probability that the number among the 25 who received a special accommodation is within 2 standard deviations of the number you would expect to be accommodated = 0.7

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