1-Suppose your director has box seats available for the next 5 home Falcons game

Question

1-Suppose your director has box seats available for the next 5 home Falcons games that she is going to randomly choose employees to receive.There are 25 employees who entered the lottery for the tickets.The first employee drawn will be given the seats for the 1st game and then won’t be eligible for the other 4 games.The 2nd employee will be given the seats for the 2nd game and then won’t be eligible for the other 3 games, and so on.How many ways can the seats be awarded?

2-Suppose that, according to a recent study, 83% of college students prefer Moes over Chipotle for dinner. In addition, 60% of college students prefer Papa Johns pizza to Dominoes. 55% of college students prefer both Moes (over Chipotles) and Papa Johns (over Dominoes). What is the probability that a randomly selected college student prefers Papa Johns, given that he or she prefers Moes?

3-Suppose requirements to be accepted to a county magnet school are to have test scores on the nationally normed MAP tests in the top 10%.If scores are normally distributed with a mean of 710 and a standard deviation of 20 for a particular grade level, what test score would be needed to qualify?

4-Suppose you know that an incoming order of 1000 widgets is 5% defective.You select 60 widgets to test.What is the probability that you find no more than 1 defect?

5-You are considering making an investment of $5,000.If the investment is successful, you will soon receive a check for $20,000.If it is unsuccessful, you will lose your money.The probability of success is 80%.What is your expected profit, if you invest?

6-Suppose water from a creek contains a particular contaminant at a rate of 100 particles per ounce.What is the probability that there are more than 1500 particles of that contaminant in 16 ounces of that creek’s water?

7-Suppose 8-oz bags of Sun Chips are filled to a mean of 8.05oz.Because of variability in the fill, the bags’ fill end up normally distributed with a standard deviation of 0.04 oz.What percentage of bags end up filled less than their labeling(i.e. less than 8 ounces)?

Explanation / Answer

1.
In the first game, an emplyoee can be selected in 25C1 = 25 ways
Similarly, in second, third, fourth and fifth game it can be done in 24, 23, 22 and 21 ways
Hence total possible ways to award the seat are 25*24*23*22*21 = 6375600

2.
P(M) = 0.83 and P(P) = 0.6
P(M and P) = 0.55

Required probability P(P|M) = P(M and P) / P(M) = 0.55/0.83 = 0.66265

3.
z-score corresponding to top 10% of normal distribution is 1.28
Test score required to qualify = mean + z*sigma = 710 + 1.28*20 = 735.6

4.
p = 0.05 n = 60
P(X<=1) = P(X=0) + P(X=1) = p^60 + 60C1*p^1*(1-p)^59
P(X<=1) = 0.05^60 + 60*(0.05)*(0.95)^59 = 0.1455

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