At a large college, 50% of students live off campus. In a random sample of 400 students, how likely is it that over 53% live off campus? Area left of z=1.2: 0.8849; of z=0.06: 0.5239.
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Solution walkthrough2:12
The sample proportion p^ changes from sample to sample. Its distribution is centred at p=0.5.
Its SD is np(1−p)=4000.5⋅0.5=200.5=0.025.
Turn 53% into a z-score: z=0.0250.53−0.5=0.0250.03=1.2.
Left of z=1.2 is 0.8849. Over 53% is the right tail: 1−0.8849=0.1151.
Traps: 0.8849 is the left side, 0.4761 uses the SD of one student, and 0.3849 is only 50% to 53%.