1. What is the probability of 3 heads and 1 tail if you toss four balanced coins at the same time? (5 points)

2. Find the probability of picking any card at random with numerical value greater than 8 in a deck of 52 playing cards. Assume an ace as having a numeric value of one, and Jack, Queen and King have a numeric value of 10. (10 pts)

3. Suppose I assigned WSJ and NYT as reading references to my class. Now suppose 45% of my students read the WSJ, 35% read the NYT and 25% read both.

a) Find the probability that a randomly selected student in my class reads at least one of them. (10 pts)

b) Find the probability that a randomly selected student in my class does not read either of them. (5 pts)

4. The probability distribution of the daily stock prices of Google for last two months are as follows:

Closing Price (X) 1875 1925 2015 2055 2111 2135

P(X) 0.15 0.25 0.25 0.20 0.13 0.02

a. Find the expected price of the Google share, using Excel. (5 pts)

b. If you paid $745 for a google share then what is your expected profit or loss? (5 pts)

c. Calculate the variance of the Google share prices in last two months, using. Excel (5 pts)

5. Assume that you work for the New York Mets and they wanted to acquire a new player whose batting average is 0.302. You calculate the variance of his hits as 0.099.

a) What is the probability he will have an average no better than 0.330 next season? (5 pts)

b) What is the probability he will have an average over 0.330 next season? (5 pts)

6.An estimate of the average GPA at SHU is 3.230 and variance is 2.68, constructed from a sample of size 150.

a) Construct a 95% confidence interval for the population mean GPA, . (10 pts)

b) Test the hypothesis H0:the population mean GPA, is 3.0.(5 pts)

please attach excel document. Thank you.