Question

At a certain university, 50% of all entering freshmen planned to major in a STEM science, technology, engineering, mathematics) discipline. A sample of freshmen is selected . What is the probability that the proportion of freshmen in the sample is between 0.484 and 0.580?

Write only a number as your answer. Round to 4 decimal places (for example 0.3748 ). Do not write as a percentage .

Answer 1

Solution:-

Assuming the n value

given that p = 0.50 , n = 36

=> P(0.484 and 0.580) = P((0.484-0.50)/sqrt(0.50*(1-0.50)/36) < z < (0.580-0.50)/sqrt(0.50*(1-0.50)/36))

= P(-0.19 < z < 0.96)

= P(z < 0.96) - P(z < -0.19)

= P(z < 0.96) - P(z < 0.19)

= 0.8315 - 0.4247

= 0.4068

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