23 In many settings, the \"rules of probability\" are just basic facts about per

Question

23 In many settings, the "rules of probability" are just basic facts about percents. The Graduate Management Admission Test (GMAT) Web site provides the following information about the undergraduate majors of those who took the test in specific years. Suppose that in a certain year: 55 % majored in business; 17 % majored in engineering; 16 % majored in the social sciences; 6 % majored in the sciences; 4 % majored in the humanities; and 4 % listed some major other than the preceding.

(a) What percent of those who took the test in a certain year majored in either engineering or the sciences?___________ % majored in engineering or science Which rule of probability did you use to find the answer? Rule 1 Rule 2 Rule 3 Rule 4

(b) What percent of those who took the test in a certain year majored in something other than business? ____________% did not major in business Which rule of probability did you use to find the answer? Rule 1 Rule 2 Rule 3 Rule 4

2.The Wechsler Adult Intelligence Scale (WAIS) is a common "IQ test" for adults. The distribution of WAIS scores for persons over 16 years of age is approximately Normal with mean 94 and standard deviation 16.

The mean value of x¯¯¯x¯ for an SRS of 55 people is .

The standard deviation of x¯¯¯x¯ (±± 0.01) for an SRS of 55 people is .

The z-score (±± 0.01) corresponding to an average WAIS score of 96 for an SRS of 55 people is .

What is the probability (±± 0.0001) that the average WAIS score of an SRS of 55 people is 96 or higher? 3

What are the mean and standard deviation of the average WAIS score x for an SRS of 60 people?

3.The Wechsler Adult Intelligence Scale (WAIS) is a common “IQ test” for adults. The distribution of WAIS scores for persons over 16 years of age is approximately Normal with mean 100 and standard deviation 15.

What are the mean and standard deviation of the average WAIS score x for an SRS of 60 people?

Mean = 100, standard deviation = 1.94 Mean = 100, standard deviation = 15 Mean = 100, standard deviation = 0.25 Mean = 13.56, standard deviation = 15

Explanation / Answer

1)

a)  What percent of those who took the test in a certain year majored in either engineering or the sciences?

% of student who majored engineering =A=17%

P(A)=0.17

% of student who majored Science =B=55%

P(B)=0.55

By the Rule 3 of probability of i.e. addition rule of disjoint event,

P(A or B)=P(A)+P(B)

P(A or B)=0.17+0.55

P(A or B)=0.72

72% majored in engineering or science.

b) What percent of those who took the test in a certain year majored in something other than business?

Let A be the number of graduates who took business as major

P(A)=55%=0.55

By Rule 4 of probability,

P(A does not occur)=1-P(A)

=1-0.55

=0.45

45% did not major in business.

As per the chegg policy i can only solve 1st question. Kindly post the other question seperately.

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