At a large local university, 40% of the students live in the dormitories. A random sample of 80 students is selected for a particular study. The probability that the sample proportion (the proportion living in the dormitories) is between 0.30 and 0.50 is what?

Question

Mathematics

Caitlin Oneill

29 May, 00:22

At a large local university, 40% of the students live in the dormitories. A random sample of 80 students is selected for a particular study. The probability that the sample proportion (the proportion living in the dormitories) is between 0.30 and 0.50 is what?

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Answers (1)

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Essence Holland · Answer 1

0.9325

Step-by-step explanation:

Given

n = sample size = 80

p = probability = 0.4

q = 1 - p = 0 ... 6

standard deviation for the proportion = √ (p * q) / n = √ (0.4*0.6) / 80 = 0.0547

for the proportion mean is 0.4

now we can find z and the probability

P (0.3
P (0.3
Using a z table

P (0.3