Question

A binomial probability experiment is conducted with the given parameters. Use technology to find the probability of x successes in the n independent trials of the experiment. Use the Tech Help button for further assistance. n= 8​, p= 0.25​, x < 4

Find P( x<4). Round to four decimal places as​ needed.

Answer 1

Answer 2

To find the probability of x successes in the n independent trials of the experiment, we can use the binomial probability formula:

P(x) = (n choose x) * p^x * (1 - p)^(n - x)

where "n choose x" is the binomial coefficient, which can be calculated as:

(n choose x) = n! / (x! * (n - x)!)

where "!" denotes the factorial function.

Using technology, we can easily calculate the probability of x<4 as follows:

Open any software or online calculator that can compute binomial probabilities, such as Wolfram Alpha, Excel, or R.

Enter the values of n, p, and x in the appropriate fields.

Use the appropriate function to calculate the binomial probability. For example, in Wolfram Alpha, you can use the following command:

Binomial[n, x] * p^x * (1 - p)^(n - x)

where you replace n, p, and x with the values given in the problem.

Round the result to four decimal places, if necessary.

Using this method, we obtain:

P(x<4) = P(x=0) + P(x=1) + P(x=2) + P(x=3)

P(x<4) = (8 choose 0) * 0.25^0 * 0.75^8 + (8 choose 1) * 0.25^1 * 0.75^7 + (8 choose 2) * 0.25^2 * 0.75^6 + (8 choose 3) * 0.25^3 * 0.75^5

P(x<4) = 0.5031 (rounded to four decimal places)

Therefore, the probability of x<4 in this binomial experiment is 0.5031.