2] The average GPA scores for the top-30 ranked graduate schools of business are

Question

2] The average GPA scores for the top-30 ranked graduate schools of business are listed here. Check for normality.

718      703      703      703      700      690      695      705      690      688

676      681      689      686      691      669      674     652      680      670

651      651      637      662      641      645      645      642      660      636

3] The average credit card debt for college seniors is $3262. If the debt is normally distributed with a standard deviation of $1100, find these probabilities.

a. That the senior owes at least $1000

b. That the senior owes more than $4000

c. That the senior owes between $3000 and $4000

4] A sample of the reading scores of 35 fifth-graders has a mean of 82. The standard deviation of the population is 15.

a. Find the best point estimate of the mean.

b. Find the 95% confidence interval of the mean reading scores of all fifth-graders.

c. Find the 99% confidence interval of the mean reading scores of all fifth-graders.

d. Which interval is larger? Explain why.

Explanation / Answer

3) MEAN = 3262

STANDARD DEVIATION = 1100

P(X>1000) =

For x = 1000, z = (1000 - 3262) / 1100 = -2.05

Hence P(x > 100) = P(z > -2.05) = [total area] - [area to the left of -2.05]

= 1 - 0.0202 = 0.9798

B)

For x = 4000, z = (4000 - 3262) / 1100 = 0.67

Hence P(x > 4000) = P(z > 0.67) = [total area] - [area to the left of 0.67]

= 1 - 0.7486 = 0.2514

C)

For x = 3000 , z = (3000 - 3262) / 1100 = 0.23 and for x = 4000, z = (4000 - 3262) / 1100 = 0.67

Hence P(3000 < x < 4000) = P(0.23 < z < 0.67) = [area to the left of z = 0.67] - [area to the left of 0.32]

= 0.7486- 0.6255 = 0.1231

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