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# Normal distribution Proportion: Z test

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Question 1 (Basic Business Statistics Tenth Edition Q 7.53.)

DiGiorno's frozen pizza has some of the most creative and likeable advertisements on television. USA Today's Ad Track claims that 20% of viewers like the ads "a lot"" (Theresa Howard, "DiGiorno Campaign Delivers Major Sales," www.usatoday.com, April 1, 2002). Suppose that a sample of 400 television viewers is shown the advertisements. What is the probability that the sample will have between:

a. 18% and 22% who like the ads "a lot"?
b. 16% and 24% who like the ads "a lot"?
c. 14% and 26% who like the ads "a lot"?
d. 12% and 28% who like the ads "a lot"?

Question 2 (Basic Business Statistics Tenth Edition, Q 7.55).

Mutual funds reported modest earnings in the first quarter of 2004. International funds, which are historically slightly more volatile than U.S. funds, had a mean return of 5.13% (Michael J. Martinez, "Mutual-fund Returns Minimal in First Quarter," Cincinnati.com, April 3, 2004). Assume that the returns of international funds were distributed as a normal random variable with a mean of 5.13 and a standard deviation of 6. If you select an individual fund from this population, what is the probability that it would have a return
a. less than 0, that is, a loss?
b. between 0 and 6?
c. greater than 10?

If you selected a random sample of 10 funds from this population, what is the probability that the sample would have a mean return
d. less than 0, that is, a loss?
e. between 0 and 6?
f. greater than 10?
g. Compare your results in parts (d) through (f) to (a) through (c).

See attached file for full problem description.