In a local university 40 of the students live in the dormito

In a 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 __________.

0.4664

0.9328

0.0336

0.6072

None of the above

Solution

? = 0.4
? = 0.0548
standardize x to z = (x - ?) / ?
P( 0.3 < x < 0.5) = P[( 0.3 - 0.4) / 0.0548 < Z < ( 0.5 - 0.4) / 0.0548]
P( -1.8258 < Z < 1.8258) = .9664 - .0336 = .9328
(From Normal probability table