1. Consider flipping a Standard US Quarter. This is an Unfair coin such that P(Tails) = 0.513 according to the best models. If you flip US Quarter 8 times you can model the number of Tails flipped as a Binomial distribution of B(8, 0.513) D. What is the Standard Deviation for the number of Tails flipped, round to the nearest thousandth. E. Compute the following to the nearest ten-thousandth: 1. P(Flip 4 tails) II. P(Flip 5 tails) III. P(Flip 3 tails) F. Without computing the Probabilities explain why P(flipped 6 or more Tails) > P(flipped 2 or fewer Tails)

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### Binomial Distribution Problem: Flipping an Unfair Coin

1. **Consider flipping a Standard US Quarter. This is an **Unfair coin** such that P(Tails) = 0.513 according to the best models. If you flip a US Quarter 8 times, you can model the number of Tails flipped as a Binomial distribution of \( B(8, 0.513) \).

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**D.** What is the Standard Deviation for the number of Tails flipped? Round to the nearest thousandth.

**E.** Compute the following to the nearest ten-thousandth:
   1. P(Flip 4 tails)
   2. P(Flip 5 tails)
   3. P(Flip 3 tails)

**F.** Without computing the Probabilities, explain why \( P(\text{flipped 6 or more Tails}) > P(\text{flipped 2 or fewer Tails}) \).

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This text introduces the concept of using a Binomial distribution to model the probability of flipping tails with a biased coin. The coin is described as having a probability of 0.513 for landing on tails. The problem involves calculations using this distribution, including the standard deviation and specific probability computations.
Transcribed Image Text:### Binomial Distribution Problem: Flipping an Unfair Coin 1. **Consider flipping a Standard US Quarter. This is an **Unfair coin** such that P(Tails) = 0.513 according to the best models. If you flip a US Quarter 8 times, you can model the number of Tails flipped as a Binomial distribution of \( B(8, 0.513) \). --- **D.** What is the Standard Deviation for the number of Tails flipped? Round to the nearest thousandth. **E.** Compute the following to the nearest ten-thousandth: 1. P(Flip 4 tails) 2. P(Flip 5 tails) 3. P(Flip 3 tails) **F.** Without computing the Probabilities, explain why \( P(\text{flipped 6 or more Tails}) > P(\text{flipped 2 or fewer Tails}) \). --- This text introduces the concept of using a Binomial distribution to model the probability of flipping tails with a biased coin. The coin is described as having a probability of 0.513 for landing on tails. The problem involves calculations using this distribution, including the standard deviation and specific probability computations.
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