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The dean of a statistics department in a certain university believes that 65% of the department’s...

The dean of a statistics department in a certain university believes that 65% of the department’s graduate positions are given to international students. A random sample of 64 graduate assistants is taken. What is the probability that the sample proportion of graduate assistants who are international students will be between 0.6 and 0.75?

Math   Statistics-And-Probability   
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Answer #1

Solution

=  [p ( 1 - p ) / n] = [(0.65 * 0.35) / 64 ] = 0.0596

= P[(0.6 - 0.65) / 0.0596 < ( - ) / < (0.75 - 0.65) / 0.0596]

= P(-0.84 < z < 1.68)

= P(z < 1.68) - P(z < -0.84)

= 0.7531

Proportion = 0.7531

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