The mean cost of getting a four-year college degree in a certain region of the c

Question

The mean cost of getting a four-year college degree in a certain region of the country is $48, 600 with a standard deviation of $8, 100. Assume costs are normally distributed. The fraction of costs for all graduates in this region that fall within plusminus $4,000 of the mean cost is? 0.5284 0.4844 0.4246 0.3758 What fraction of sample means from samples of size n = 16 graduates fall within plusminus $4,000 from the population mean? 0.8904 0.9198 0.9398 0.9522 In repeated sampling of n = 25 graduates, the interval which contains the middle 95% of sample mean costs is: x_1 = _____ x_2 = _____ $41, 615 $55, 585 $42, 567 $54, 633 $43, 837 $53, 363 d $45, 425 $51, 775 In another region 5% of the x values from samples of size n = 25 are under $48,000 and 5% are over $57,000. From this sampling distribution information we can conclude that the population mean cost of a four-year college degree is mu = _____ $50, 500 $51, 500 $52, 500 $53, 500 In the previous question, the population standard deviation is sigma = $12, 980 $13, 720 $14, 240 $14, 760

Explanation / Answer

Question 9

We have to find

P(48600 – 4000 < X < 48600 + 4000) = P(44600<X<52600)

P(44600<X<52600) = P(X<52600) – P(X<44600)

Z = (X – mean) / SD

Z = (52600 – 48600) / 8100 = 0.49382716

Z = (44600 – 48600)/8100 = -0.493827

P(X<52600) = P(Z< 0.49382716) = 0.689286

P(X<44600) = P(Z< -0.493827) = 0.310714125

P(44600<X<52600) = P(X<52600) – P(X<44600)

P(44600<X<52600) = 0.689286 - 0.310714125 = 0.378572

Required answer: d. 0.3758

Question 10

We have to find

P(48600 – 4000 < X < 48600 + 4000) = P(44600<X<52600)

P(44600<X<52600) = P(X<52600) – P(X<44600)

Z = (Xbar - µ) / [ / sqrt(n)]

Z = (52600 – 48600) / [8100/sqrt(16)] = 1.975309

P(Z< 1.975309) = 0.975883

Z = (44600 – 48600) / [8100/sqrt(16)] = -1.975308642

P(Z<-1.975308642) = 0.024116567

P(44600<X<52600) = 0.975883 - 0.024116567 = 0.951767

Required Answer: d. 0.9522

Question 11

Z = (Xbar - µ) / [ / sqrt(n)]

(Xbar - µ) = Z*[ / sqrt(n)]

Xbar = µ + Z*[ / sqrt(n)]

Middle area = 95%

Remaining area = 1 – 0.95 = 0.05

Area at left side = 0.05/2 = 0.025

Area at right side = 0.05/2 = 0.025

Critical Z value = 1.96

Xbar = µ + Z*[ / sqrt(n)]

Xbar = 48600 + 1.96*[8100/sqrt(25)]

Xbar = 51775.2

Xbar = 48600 - 1.96*[8100/sqrt(25)]

Xbar = 45424.8

Correct answer: d. $45425, 51,775

Question 12

Xbar – Z*SD/sqrt(n) = 48000

Xbar + Z*SD/sqrt(n) = 57000

Z = 1.96

Z*SD/sqrt(n) = 1.96*8100/sqrt(25) = 1.96*8100/5 = 3175.2

Xbar = 48000 + 3175.2 = 51500

Required answer = b. 51500

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