1. The net profit of an investment is normally distributed with a mean of $10,000 and a standard deviation of $5,000. The probability that the investor's net gain will be at least $5,000 is _____________.

a) 0.4967
b) 0.8413
c) 0.1859
d) 0.3413

Answer: b) 0.8413

Mean=M = $10,000
Standard deviation =s= $5,000
x= $5,000
z=(x-M )/s= -1 =(5000-10000)/5000
Cumulative Probability corresponding to z= -1 is= 0.1587
Or Probability corresponding to x< 5000.00 is Prob(Z)= 0.1587
Therefore probability corresponding to x> 5000.00 is 1-Prob(Z)= 0.8413 =1-0.1587
0r= 84.13%

2. A company believes that it controls more than 30% of the total market share for one of its products. To prove this belief, a random sample of 144 purchases of this product are contacted. It is found that 50 of the 144 purchased this company's brand of the product. If a researcher wants to conduct a statistical test for this problem, the test would be _______.

a) an alpha test
b) a one-tailed test
c) a finite population test
d) a two-tailed test

Answer: b) a one-tailed test

The alternative hypothesis is that the company has more than 30% of market share. Thus we are looking for area in the right tail