1. Experience has shown that approximately 1/100 (p = 0.01) manufactured DVDs is defective. Suppose that you take a sample of 5 DVDs from the production line.
(A) Calculate the probability that zero DVDs out of the five are defective.
(B) Calculate the probability that one DVD out of the five is defective.
(C) Calculate the probability that two or more DVDs in the sample of five are defective. Can we conclude with a high degree of certainty that something is wrong with the production process if two or more are found to be defective in such a sample? Why or why not?
2. Your friend offers an interesting wager. He offers to pay you $30 if you can flip 5 heads in a row on a fair coin. You only pay $1 if you lose. You’re considering whether to take the wager. You decide to take the wager only if it is a smart move according to probability (i.e. the wager must have a positive expected value).
(A) Calculate the probability of flipping 5 straight heads.
(B) Calculate the expected value of the wager. Hint: Use results from (A) and
P(win wager)*(Amount you would win) + P(lose wager)*(-Amount you would lose)
(C) Should you accept the wager? Why or why not?
(D) Calculate the minimum amount you would need to be offered to take the bet (use a little bit of algebra and the above equation).
3. (Use Excel) In the game of blackjack as played in casinos, the dealer has the advantage. Most players do not play very well. Let’s say the probability of a player winning a random hand is about 45%. Find the probability that the average player: (A) Wins twice in five hands.
(B) Wins ten or more times in 25 hands.
(C) Wins more than half of the next 50 hands.
Assuming the random variable Z is normally distributed with a mean of 0 and a standard deviation of 1 (standard normal variable), calculate:
4. (A) P (Z (B) P (Z>2.45)
(C) P (Z > – 2.45)
(D) P (Z (E) P (-2.45
5. As an analyst for a mobile device manufacturer, you have noticed that customers between 18 and 24 years of age spend an average of 325 minutes per month watching video on their device. The standard deviation of the time they spend is 50 minutes. Assuming the time spent watching video by this consumer demographic is approximately normally distributed, find the following probabilities:
(A) A randomly selected 18-24 year-old customer watches video for less than 300 minutes.
(B) Find the probability that a randomly selected 18-24 year old customer watches video for more than 400 minutes.
(C) Find the probability that a randomly selected 18-24 year old customer watches video for less than 400 minutes.
(D) Find the probability that a randomly selected 18-24 year old customer watches video for between 300 and 400 minutes.
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