A candy company claims that 13% of its plain candies are orange, and a sample of 100 such candies is randomly selected.

Find the mean and the standard deviation for the number of orange candies in such groups of 100.

I do not get the formula to figure this out Someone, please help! Thank you

Well, if you need help with candy, you've come to the right place! Let's calculate the mean and standard deviation for the number of orange candies in a sample of 100 plain candies.

First, we'll start with the mean. The mean is simply the expected value, which can be found by multiplying the probability of an event by the number of trials. In this case, the probability of selecting an orange candy is 13% or 0.13, and the number of candies in each sample is 100. So, the mean is:

Mean = 0.13 * 100 = 13

Therefore, the mean number of orange candies in a sample of 100 is 13.

Now, let's move on to the standard deviation. The formula for the standard deviation for a binomial distribution (like this one) is:

Standard Deviation = sqrt(n * p * q),

where n is the number of trials (100 in this case), p is the probability of success (0.13), and q is the probability of failure (which is 1 minus the probability of success, so 1 - 0.13 = 0.87).

Standard Deviation = sqrt(100 * 0.13 * 0.87)
Standard Deviation ≈ 3.405

Therefore, the standard deviation for the number of orange candies in a sample of 100 is approximately 3.405.

I hope this helps, and don't forget to share the candy!

To find the mean and standard deviation for the number of orange candies in a sample of 100, we can use the formulas for the mean and standard deviation of a binomial distribution.

1. Mean (μ):
The mean of a binomial distribution is given by the formula:
μ = n * p
where n is the number of trials (sample size) and p is the probability of success (in this case, the probability of getting an orange candy).

Substituting the values, we have:
n = 100 (sample size)
p = 0.13 (probability of getting an orange candy)

μ = 100 * 0.13 = 13

Therefore, the mean number of orange candies in a sample of 100 is 13.

2. Standard Deviation (σ):
The standard deviation of a binomial distribution is given by the formula:
σ = √(n * p * (1 - p))
where n is the number of trials (sample size) and p is the probability of success (in this case, the probability of getting an orange candy).

Substituting the values, we have:
n = 100 (sample size)
p = 0.13 (probability of getting an orange candy)

σ = √(100 * 0.13 * (1 - 0.13))

Now, calculate (1 - 0.13):
(1 - 0.13) = 0.87

Substituting this value back into the formula, we have:
σ = √(100 * 0.13 * 0.87)

Now, perform the further calculation:
σ = √(11.31)

Finally, compute the square root:
σ ≈ 3.36 (rounded to two decimal places)

Therefore, the standard deviation for the number of orange candies in a sample of 100 is approximately 3.36.

To find the mean and the standard deviation for the number of orange candies in a sample of 100 plain candies, you can use the binomial distribution formula. The binomial distribution is appropriate when there are two possible outcomes (in this case, orange or non-orange) and the probability of success (orange candy) remains constant for each trial.

The mean, denoted as μ (mu), for a binomial distribution is calculated as:
μ = n * p
where n is the number of trials (sample size) and p is the probability of success (proportion of orange candies).

In this case, n = 100 and p = 0.13.
So, μ = 100 * 0.13 = 13.

The standard deviation, denoted as σ (sigma), for a binomial distribution is calculated as:
σ = √(n * p * (1 - p))

Using the same values as before, σ = √(100 * 0.13 * (1 - 0.13)).

Let's calculate this value step by step:

Step 1: Multiply p by (1 - p)
0.13 * (1 - 0.13) = 0.13 * 0.87 = 0.1131

Step 2: Multiply the result by n
0.1131 * 100 = 11.31

Step 3: Take the square root of the result
√(11.31) ≈ 3.36

Therefore, the mean is 13 and the standard deviation is approximately 3.36 for the number of orange candies in a sample of 100 plain candies.