Admissions records at MIT indicates that 6.7% of the graduate students enrolled

ID: 3370419 • Letter: A

Question

Admissions records at MIT indicates that 6.7% of the graduate students enrolled are from Canada.

What is the minimum sample size for which the Central Limit Theorem applies in this case?

A) n=30. B) n=40. C) n=50. D) n=100. E) n=200.

Find the mean and standard error of the sample proportion of Canadian students in random samples of 100 graduate students at MIT.

A) ˆp=0.067,SE=0.0625. B) ˆp=0.067,SE=0.006. C) ˆp=0.067,SE=0.025. D) ˆp=0.670,SE=0.250. E) ˆp=0.067,SE=0.0067.

Roughly what percentage of samples of 100 randomly selected graduate students at MIT will have at least 10% of students from Canada?

A) 5%. B) 6.7%. C) 10%. D) 18%. E) 25%.

For a N (0, 1) density, what is the area to the left of z = ?1.645.

A) 2.5%. B) 3.5%. C) 5%. D) 10%. E) 11%.

For a N (0, 1) density, what is the area outside of the interval z = ?2.326 and z = 1.282.

A) 2.5%. B) 3.5%. C) 5%. D) 10%. E) 11%.

1) Irrespective of the proportion of students enrolled, the Central Limit Theorem is only applicable for a sample size which is at least 30.

So, n=30 will be our answer which is option (A)

2) n = 100

Mean = 0.067 which is an indication of 6.7 students out of 100

SE = sqrt(p(1-p)/n)

So, we have SE = sqrt(0.067*0.933/100) = 0.025

That will be option -(C)

3) This will be nothing but 6.7% again

4) Standard normal distribution-

P(Z<-1.645) = 0.05 = 5%

This will be option (C)

5) P(Z<-2.326 and Z>1.282) = P(Z<-2.326) + P(Z>1.282) = 0.0102 + 0.1003 = 0.1105= 11%

This will be option (E)

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