SOLUTION: Sixty five percent of 12th graders attend school in a particular urban district. If a sample of 450 12th grade children is selected. 1. Find the probability that at least 290 a

Question 1121525: Sixty five percent of 12th graders attend school in a particular urban district. If a sample of 450 12th grade children is selected.
1. Find the probability that at least 290 are actually enrolled in the school
2. Find the probability that less than 300 are actually enrolled in the school.
3. Find the probability that more than 280 are actually enrolled in the school.

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Convert this to a normal approximation
np=mean or 450*0.65 or 292.5
sd=sqrt (V), where V=292.5*0.35=102.375, so sd=10.12
use 289.5 as continuity correction factor for 290
(289.5-292.5)/10.12 is the z value for a, and that is -0.30
The probability z>-0.30 is 0.6179
fewer than 300 use (299.5-292.5)/10.12, and z < 0.69 Probability z < 0.69 is 0.7549
more than 280 use 280.5 (280.5-292.5)/10.12 and z > -1.19, with probability of 0.8830

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