Question

100 POINTS!!!! Use the data stated to complete this portion of the project.

1. Numbers listed in numerical order.

342, 518, 535, 605

2. Context of the question.

The bag contains 605 red, 342 blue, 518 green, and 535 yellow tokens. A token is selected at random and then replaced.

3. The mean of the data.

518

4. Minimum and maximum in the data.

342 and 602


Questions/requests that need to be answered:

1. Create a frequency distribution table for your data.

2. Create a probability distribution table for your data.

3. Label the distribution curve with the mean, and 6 standard deviations for your data set.

Answer 1

Explanation:

Distribution curve:

The distribution curve for this data set would be a normal distribution, as the data is approximately symmetrical and the mean is close to the center of the data. The mean of the data is 518, and 6 standard deviations from the mean would be:

Lower limit: 518 - (6 x standard deviation)

Upper limit: 518 + (6 x standard deviation)

To calculate the standard deviation, we first need to calculate the variance:

Variance = ∑(xi - μ)^2 / N

Where xi represents each value in the data set, μ is the mean, and N is the total number of values.

Using the values given, we can calculate the variance:

Variance = [(342 - 518)^2 + (518 - 518)^2 + (535 - 518)^2 + (605 - 518)^2] / 4

= 24,270

The standard deviation is the square root of the variance:

Standard deviation = √24,270

= 155.8

Therefore, the lower limit of the distribution curve would be 518 - (6 x 155.8) = 218.4, and the upper limit would be 518 + (6 x 155.8) = 817.6.