# Would it be unusual for an data value to be more extreme than 4.76 standard deviations from the mean?  Explain using probability.Would it be unusual for a data value to be more extreme than -1.36 standard deviations from the mean?  Explain using probability.For 9 trials that follow a binomial distribution with the probability of failure at 8%, find the probability of exactly 6 successes.Find and interpret the expected value of a \$20 bet on red and \$40 bet on black for one spin of the roulette wheel.

Question
1. Would it be unusual for an data value to be more extreme than 4.76 standard deviations from the mean?  Explain using probability.
2. Would it be unusual for a data value to be more extreme than -1.36 standard deviations from the mean?  Explain using probability.
3. For 9 trials that follow a binomial distribution with the probability of failure at 8%, find the probability of exactly 6 successes.
4. Find and interpret the expected value of a \$20 bet on red and \$40 bet on black for one spin of the roulette wheel.
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Step 1

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Step 2

1.

According to Chebyshev’s inequality, one can find the unusual value.

The probability of a data value to be more extreme than 4.76 standard deviations from the mean is less than 0.04. It can be considered as unusual data value because it is unlikely to happen.

According to empirical normal probability, a data value which is far away from the three standard deviations of the mean can be considered as unusual value and it has less probability of occurrence.

Step 3

2.

According to Chebyshev’s inequality, we have

The probability of a data value to be more extreme than –1.36 standard deviations from the mean is 0.54. It cannot be considered as unusual data value because the probability of happening is hi...

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