Reference no: EM132230310

Assignment -

Assume these numbers are the population of interest: {0, 1, 1, 6, 9, 10, 14, 14, 17}

1. Calculate the mean, the range, the Sum of Squares, the variance and the standard deviation for this population.

2. I've drawn a sample from the above population: {0, 1, 6, 9}

a) Calculate the Sum of Squares, the variance and the standard deviation for this sample.

b) Compare the standard deviation from the sample to the standard deviation of the population (calculated in #1). Is the sample standard deviation bigger or smaller? Why is this the case?

3. A popular dating site is about to buy an existing singles app and incorporate it into their system. The singles app uses an attractiveness rating system where users rate how appealing they find the other users. For parts C and D, use the figure at the bottom of the document.

Here is the population of attractiveness scores from the singles app:

{2, 2, 4, 4, 4, 8, 10, 10, 12, 12, 12, 16} µ = 8, σ = 4

a) Transform the population of scores into z-scores. Report the µ and σ for the new standardized distribution.

b) The owners of the dating site want the rating system transformed into a standard distribution with µ = 10 and σ = 2. Calculate and present this distribution for the population.

c) If we assumed that the population is normally distributed, what percentage of people would be rated below an 8 on the ORIGINAL singles app scale?

d) Assuming a normal distribution, what percentage of people would be rated below an 8 on the NEW STANDARDIZED scale?

Note: For each calculation, only the answer is required. But showing the formula used to make the calculation will allow you to keep some points if your calculation is incorrect. In the case of decimals, round to the nearest hundredths place (ex: 9.37).

Attachment:- Assignment Files.rar