Question 75466: Q1. A final exam in math 160 has a mean of 73 with standard deviation 7.8. If 24 students are randomly selected, find the probability that the mean of their test score is greater than 78.
Q2.For the binomial distribution with the given values for n and p, state whether or not it is suitable to use the normal distribution as an approximation. n = 16 and p = 0.5
Q3. This is the same as question 1, but find the probability that the mean of their test scores is LESS than 70
Q4. Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution. With n = 20 and p = 0.06, estimate p (fewer than 8).
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Q1. A final exam in math 160 has a mean of 73 with standard deviation 7.8. If 24 students are randomly selected, find the probability that the mean of their test score is greater than 78.
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z(78)=(78-73)/7.8/sqrt(24)=3.14
P(z>3.14)=0.0008448059....
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Q2.For the binomial distribution with the given values for n and p, state whether or not it is suitable to use the normal distribution as an approximation. n = 16 and p = 0.5
The answer to this depends on the conditions listed in your text for using
a normal approximation on a binomial problem.
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Q3. This is the same as question 1, but find the probability that the mean of their test scores is LESS than 70
z(70)=(70-73)/7.8/sqrt(24)=-1.88442228...
P(z<-1.88442228...)=0.02975...
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Q4. Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution. With n = 20 and p = 0.06, estimate
P(fewer than 8).
Z(8)=(8-20*0.06)/sqrt(20*0.06*0.94)=6.8/1.06207=6.40257
P(z<6.40257)=0.9999
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Cheers,
Stan H.
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