SOLUTION: 15. The IQs of 600 applicants of a certain college are approximately normally distributed with a mean of 115 and a standard deviation of 12. If the college requires an IQ of at lea

Question 47920: 15. The IQs of 600 applicants of a certain college are approximately normally distributed with a mean of 115 and a standard deviation of 12. If the college requires an IQ of at least 95, how many of these students will be rejected on this basis regardless of their other qualifications?
9. Assume the 2 out of 5 shipments coming from a particular supplier do not arrive on time. What is the probability that among 8 shipments which this supplier sends,
a.) Exactly 3 will not arrive on time?
b.) Less than 3 will not arrive on time?
c.) Exactly 6 will arrive on time?

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
15. The IQs of 600 applicants of a certain college are approximately normally distributed with a mean of 115 and a standard deviation of 12. If the college requires an IQ of at least 95, how many of these students will be rejected on this basis regardless of their other qualifications?
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Find the area below 95 on a normal curve with mean 115 and standard deviation
of 12.
Convert 95 to a z score of -1.666666...
Find the area below -1.6666.. using your z-chart.
Answer: 0.0478 or 4.8%
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9. Assume the 2 out of 5 shipments coming from a particular supplier do not arrive on time.
This is a binomial problem with P(not on time)=2/5
What is the probability that among 8 shipments which this supplier sends,
a.) Exactly 3 will not arrive on time?
P(x=3)= 8C3(2/5)^3(3/5)5=0.2787
------------
b.) Less than 3 will not arrive on time?
P(x<3)=P(x=0 + x=1 + x=2)= 0.3154
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c.) Exactly 6 will arrive on time?
P(6 on time) = 8C6(3/5)^6(2/5)^2 = 0.2090
----------------
Cheers,
Stan H.

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