Construct a binomial probability distribution with the given...

Construct a binomial probability distribution with the given parameters. Use n = 6 and p = 0.6 to complete parts (a) through (d) below. (a) Complete the probability distribution with the given parameters. x p(x) 0 1 2 3 4 5 6 (b) Compute the mean and standard deviation of the random variable using ?x = ?[x·P(x)] and ?x^2 = ?[x^2·P(x)] ? ?x^2. (c) Round to four decimal places as needed. (d) Round to two decimal places as needed. P(X ? ?) (Round to two decimal places as needed) P(X ? ?) (Round to two decimal places as needed)

Transcript

00:01 Here we consider a binomial distribution based on six trials and probability of success, 0 .6.

00:10 And for part a we are asked to construct the binomial probability distribution.

00:15 So generally the probability function for the binomial random variable is given by this formula, where x can be any integer from 0 up to n, in this case n is 6.

00:35 And so for example, for the first probability, it's the probability that x is equal to 0.

00:41 The probability function simplifies to 1 minus p, which is 0 .4, to the exponent n, which is 6.

00:48 And this comes out to a probability of approximately 0 .0041.

01:01 Now this can be a bit tedious to do for all 7 of these probabilities.

01:05 So let's use excel to do this.

01:08 So in excel, if in column a we put all of the values that x can take on from 0 up to 6, and then in column b, we're going to use the binomial distribution function.

01:25 So for the first row, start with an equal sign.

01:27 Binomial distribution function is what we want to select.

01:31 For the number of successes, i select the cell in column a.

01:35 In this case, it happens to be zero.

01:37 And i hit comma.

01:39 The number of trials is 6.

01:41 Probability of success is 0 .6.

01:44 For the cumulative argument, we enter false because we want the probability that x is exactly equal to whatever is in column a.

01:50 And hit enter, and so we get the same result as we calculated for x equals 0.

01:58 Then we can drag this handle down at the bottom right for all possible values of x.

02:04 And then in column b we have all of the probability masses for all possible values of the random variable x...

Question

Please give Ace some feedback