SOLUTION: Could you please help me to solve this problem? A binomial probability distribution has n = 15 trials with the probability of success on each trial is p = .65. Calculate the fo

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Question 449786: Could you please help me to solve this problem?
A binomial probability distribution has n = 15 trials with the probability of success on each trial is p = .65. Calculate the following.
a. The mean,, of the distribution
b. The standard deviation of the distribution
c. The probability of 10 successes
d. The probability of 10 failures
e. The probability of at least 14 successes
Must show work
Answer by stanbon(75887) (Show Source):
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Could you please help me to solve this problem?
A binomial probability distribution has n = 15 trials with the probability of success on each trial is p = .65. Calculate the following.
a. The mean,, of the distribution:: np = 15*0.65
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b. The standard deviation of the distribution:: sqrt(npq) = sqrt(15*0.65*0.35)
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c. The probability of 10 successes:: 15C10(0.65)^10*(0.35)^5
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d. The probability of 10 failures::: 15C10(0.35)^10*(0.65)^5
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e. The probability of at least 14 successes::
Ans: P(14<= x <= 15) P(x = 14) + P(x = 15) = 15C14(0.65)^14*(0.35)+(0.65)^15
= 15*0.0024*(0.35) + 0.0016
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= 0.01416
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Cheers,
Stan H.
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