# Normal distribution Proportion: Z test

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.

© BrainMass Inc. brainmass.com June 3, 2020, 7:33 pm ad1c9bdddfhttps://brainmass.com/statistics/z-test/normal-distribution-proportion-z-test-103575

#### Solution Summary

Determination of Critical value, Significance level, p value for Z test.