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.
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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.