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8 Cards in this Set
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"Fruit Snax" come in pouches of 10 snack pieces per pouch, and the pouches are generally sold by the box (4 pouches). The snack pieces come in 5 different fruit flavors, and usually each pouch contains at least one piece from each of the flavors. The website of the company that manufactures the product says that equal numbers of the 5 flavors are produced and that the pouches are filled in such a way that each piece added is equally likely to be any one of the 5 flavors. If the information on the company's website is accurate, what proportion of the population of snack pieces is mango flavored?
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If each of the flavors occurs equally, then the proportion of mango pieces is 1/5 of 0.20
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"Fruit Snax" come in pouches of 10 snack pieces per pouch, and the pouches are generally sold by the box (4 pouches). The snack pieces come in 5 different fruit flavors, and usually each pouch contains at least one piece from each of the flavors. The website of the company that manufactures the product says that equal numbers of the 5 flavors are produced and that the pouches are filled in such a way that each piece added is equally likely to be any one of the 5 flavors. If the information on the company's website is accurate, on average, how many mango flavored pieces should be expected in a pouch of 10 snack pieces?
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If the proportion of mango pieces is 1/5, then a random sample of 10 pieces should have (1/5)(10) = 2 mango flavored pieces on average.
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"Fruit Snax" come in pouches of 10 snack pieces per pouch, and the pouches are generally sold by the box (4 pouches). The snack pieces come in 5 different fruit flavors, and usually each pouch contains at least one piece from each of the flavors. The website of the company that manufactures the product says that equal numbers of the 5 flavors are produced and that the pouches are filled in such a way that each piece added is equally likely to be any one of the 5 flavors. If the information on the company's website is accurate, what is the chance that a pouch of 10 would have no mango flavored pieces? Is it reasonable that this just happens by chance sometimes?
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The chance of selecting a single non-mango piece is 4/5 or 0.80. If the selection of each piece is independent, then the chance of getting 10 non-mango pieces is about 0.1074. So, yes, it is reasonable that a single pouch may not have a single mango flavored piece in it sometimes.
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"Fruit Snax" come in pouches of 10 snack pieces per pouch, and the pouches are generally sold by the box (4 pouches). The snack pieces come in 5 different fruit flavors, and usually each pouch contains at least one piece from each of the flavors. The website of the company that manufactures the product says that equal numbers of the 5 flavors are produced and that the pouches are filled in such a way that each piece added is equally likely to be any one of the 5 flavors. If the information on the company's website is accurate, what is the chance that an entire box of 4 pouches would have no mango flavored pieces?
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An entire box would consist of 40 snack pieces. As previously calculated, the chance of selecting a single non-mango flavored piece is 4/5. If the selection of each piece is independent, then the chance of getting 40 non-mango flavored pieces is about 0.001.
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"Fruit Snax" come in pouches of 10 snack pieces per pouch, and the pouches are generally sold by the box (4 pouches). The snack pieces come in 5 different fruit flavors, and usually each pouch contains at least one piece from each of the flavors. The website of the company that manufactures the product says that equal numbers of the 5 flavors are produced and that the pouches are filled in such a way that each piece added is equally likely to be any one of the 5 flavors. If the information on the company's website is accurate, would you be concerned that the company's claims were false if you encountered a box with no mango flavored pieces in any of the pouches? Or would you say that this event is not surprising? Explain.
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A 0.001 chance of receiving no mango flavored pieces is a 1 in 10,000 chance. This means that it is not impossible, but is uncommon or rare. Therefore, the company's policies shouldn't be questioned because despite the low probability, it can still happen.
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Andrew wants to sell his car. He spends $300 to advertise the sale of the car. If the car sells in two months, andrew earns $800. Otherwise, he loses the listing. If there is a 50% chance that the car will sell in 2 months, what is the expected payoff?
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E= ($800)(0.5)-($300)= $100.
The expected payoff is $100. |
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Three friends decide to play a dice game. If it lands on 1, then they win $5. If it lands on 6, they win $10. If it lands on any other number, they lose $3. Is this game fair?
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The dice has 6 sides. First, we find the probability distribution for a single roll and the amount of dollars they win. E(x)= 5(1/6)+10(1/6)+(-3)(4/6) = 1/2. The expected value is not 0, therefore the game is not fair. They will lose about 50 cents for a single roll on average.
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A team has the choice of hitting a short field goal, running for a touchdown, or passing for a touchdown. A field goal recieves 3 points and a touchdown receives 6. The coach has run the statistics on what would be best from their field position. The strategies are: field goal success: 75.6%, run for touchdown success: 63.4% and throw for touchdown success: 84%. If the team gets 15 chances to score from that field position this season, which strategy would result in statistically the most points?
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We have to calculate the total number of predicted points they could amass.
Field goals: 15*3*0.756= 34 points Running: 15*6*0.634= 57 points Passing: 15*6*0.84 =76 points. Based on this, they would score the most points by passing for a touchdown each time they had the chance. |
