Question

A) A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment. n = 12, p = 0.35, x = 2 P(2) = ? B) A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment. n = 30, p = 0.03, x = 2 P(2) = ? C) A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment. n = 6, p = 0.65, x = 2 P(2) = ? D) A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment. n = 9, p = 0.9, x ≤ 3 The probability of x ≤ 3 successes is: ?

          A) A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment.
n = 12, p = 0.35, x = 2
P(2) = ?

B) A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment.
n = 30, p = 0.03, x = 2
P(2) = ?

C) A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment.
n = 6, p = 0.65, x = 2
P(2) = ?

D) A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment.
n = 9, p = 0.9, x ≤ 3
The probability of x ≤ 3 successes is: ?

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Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Robin Corrigan

10/03/2023

Step 1

The formula for the binomial probability is: $P(x) = \binom{n}{x} p^x (1-p)^{n-x}$ where $n$ is the number of trials, $p$ is the probability of success, $x$ is the number of successes, and $\binom{n}{x}$ is the number of combinations of $n$ items taken $x$ at a Show more…

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A) A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment. n = 12, p = 0.35, x = 2 P(2) = ? B) A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment. n = 30, p = 0.03, x = 2 P(2) = ? C) A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment. n = 6, p = 0.65, x = 2 P(2) = ? D) A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment. n = 9, p = 0.9, x ≤ 3 The probability of x ≤ 3 successes is: ?

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00:01 In this exercise we consider four binomial probability experiments.

00:05 We call that a binomial random variable, we're denoting x, is the number of successes in a fixed number of independent bernoulli trials.

00:17 And each binomial distribution is defined by its two parameters.

00:21 We have n as the number of trials, and p as the probability of success on each trial.

00:26 The random variable is x.

00:30 So for part a, we have a binomial with 12 trials and a 0 .35 probability of success.

00:36 We want to know the probability of two successes.

00:40 The probability function for the binomial, in general terms, is given by this formula.

00:59 So for part a, if we want to solve the probability of x equals 2, using the probability function we have 12 choose 2 times 0 .35 to the exponent 2 times 0 .65 to the exponent 10.

01:23 And this comes out to 0 .1088.

01:30 For b, we have a binomial with 30 trials and a 0 .03 probability of success.

01:36 And we want the probability of two successes.

01:40 So we can calculate this as 30 choose 2.

01:47 Actually, let's use excel to solve this one, just for a change.

01:51 So if we use excel, start the computation with an equal sign.

01:56 We want to use the binomial distribution function, so we select that function.

02:00 For the number of successes, we enter 2.

02:03 The number of trials is 30, it's a 0 .03 probability of success...

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