Question

If x is a binomial random variable with n=10 and p=0.8, what is the probability that x is equal to 4?

Answer 1

The probability that x is equal to 4 in a binomial distribution with n=10 and p=0.8 is 0.006048.

Step-by-step explanation:

To find the probability that x is equal to 4 in a binomial distribution with n=10 and p=0.8, we can use the probability mass function (PMF) of the binomial distribution.

The PMF is given by: P(x) = (n choose x) * p^x * (1-p)^(n-x)

Substituting the given values, we have: P(4) = (10 choose 4) * 0.8^4 * 0.2^6 = 0.006048

Answer 2

Which methods of obtaining binomial probabilities are you familiar with? You could use a TI-83 or TI-84 Plus calculator's binompdf( ) function, or obtain this probability from a binomial probability table, or calculate the probability using the appropriate formula.

Using my TI-83 Plus calculator: type in binompdf(10, 0.8, 4). My calculator returns the result 0.0055. This is a "small" probability.

As an example, try letting n=8 instead of 4: binompdf(10, 0.8, 8). My calculator returns the result 0.3020.

One more example: use the "binomcdf" function to produce all nine probabilities (x=0 through x=8): {1.02E(-7), 4.096E(-6), ...... 0.0055, 0.0264, 0.0881, 0.2013, .3020, 0.2684, 0.1774}. The outcome "8" has the greatest probability. Were you to add up these 11 probabilities, the sum would be 1.