Problem

Suppose that X is a random variable with the binomial distribution with n=16 and p=0.6853. Calculate P(X=10). If rounding is necessary, round as indicated on the formula sheet.

Answer

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Answer

Final Answer: The probability P(X=10) is approximately 0.1777.

Steps

Step 1 :We are given that X is a random variable with the binomial distribution with n=16 and p=0.6853. We are asked to calculate P(X=10).

Step 2 :The binomial distribution is given by the formula: P(X=k)=(nk)pk(1p)nk where: n is the number of trials, k is the number of successful trials, p is the probability of success on each trial, and (nk) is the binomial coefficient, which can be calculated as n!k!(nk)!.

Step 3 :In this case, we have n=16, k=10, and p=0.6853. We can substitute these values into the formula to find P(X=10).

Step 4 :First, we calculate the binomial coefficient (nk), which is (1610)=8008.0.

Step 5 :Next, we substitute n=16, k=10, p=0.6853, and (nk)=8008.0 into the formula to get P(X=10)=8008.0(0.6853)10(10.6853)1610=0.17770998905405114.

Step 6 :Final Answer: The probability P(X=10) is approximately 0.1777.

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