Question

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Exercises for Chapter 7: Sa mpling Distributions I entrance exam at an MBA program in the Central Valley of doo Are scores on the GMAT entrance exam a discrete or a continuous variable? What is the probability that a randomly selected application will report a GMAT score of less than 600? a. b.

Answer 1

Solution:-

7.1)

Mean = 591, S.D = 42

a) The scores on GMAT entrance exam are continuous variable.

b) The probability that scores will be less than 600 is 0.5848.

x = 600

By applying normal distribution:-

$z = \frac{x-\mu }{\sigma }$

z = 0.2143

P(z < 0.2143) = 0.5848

c) The probability that scores from sample of 50 will be less than 600 is 0.9351.

x = 600

By applying normal distribution:-

$z = \frac{x-\mu }{\frac{\sigma }{\sqrt{n}}}$

z = 1.515

P(z < 1.515) = 0.9351

d) The probability that scores from sample of 100 will be less than 600 is 0.9839.

x = 600

By applying normal distribution:-

$z = \frac{x-\mu }{\frac{\sigma }{\sqrt{n}}}$

z = 2.143

P(z < 2.143) = 0.9839