Question 2 A weekend TV game show called rolling a dice is running each week. For each roll, if the dice shows an odd number the participate earns 40 dollars and otherwise he gets nothing. Each participate can roll the dice 5 times. Let X denote the number times the dice shows an odd number. a) Calculate the average earning of a participate. b) Calculate the probability that the dice shows more than one odd number. c) Under appropriate condition, a Binomial random variable X can be approximated by a Normal random variable Y with the same mean and standard deviation. In doing so, we need to apply a continuity correction. That is P(X > a) × P(Y > a + 0.5). Calculating the probability that x > 1 by using Normal approximation with continuity correction (for all intermediate steps, please keep your result to two decimal places).
Question 2 A weekend TV game show called rolling a dice is running each week. For each roll, if the dice shows an odd number the participate earns 40 dollars and otherwise he gets nothing. Each participate can roll the dice 5 times. Let X denote the number times the dice shows an odd number. a) Calculate the average earning of a participate. b) Calculate the probability that the dice shows more than one odd number. c) Under appropriate condition, a Binomial random variable X can be approximated by a Normal random variable Y with the same mean and standard deviation. In doing so, we need to apply a continuity correction. That is P(X > a) × P(Y > a + 0.5). Calculating the probability that x > 1 by using Normal approximation with continuity correction (for all intermediate steps, please keep your result to two decimal places).
Transcribed Image Text:Question 2
A weekend TV game show called rolling a dice is running each week. For each roll, if the
dice shows an odd number the participate earns 40 dollars and otherwise he gets nothing.
Each participate can roll the dice 5 times. Let X denote the number times the dice shows an
odd number.
a) (2
Calculate the average earning of a participate.
b)
Calculate the probability that the dice shows more than one odd number.
c)
approximated by a Normal random variable Y with the same mean and standard
deviation. In doing so, we need to apply a continuity correction. That is
Under appropriate condition, a Binomial random variable X can be
P(X > a) × P(Y > a + 0.5).
Calculating the probability that X > 1 by using Normal approximation with
continuity correction (for all intermediate steps, please keep your result to two
decimal places).
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