The 15 most populous states in the United States have an average population of 141.51 million, with a standard deviation of 87.49 million. Virginia and Washington have populations of 83.83 million and 71.70 million, respectively. Texas and Pennsylvania have z-scores of 1.52 and −0.15, respectively. Part A: List these four states in order from smallest to largest populations. (5 points)

Part B: Mathematically explain your reasoning and be sure to include all necessary calculations. (5 points) (10 points)

Answer and Step-by-step explanation:

Part A: The fours states in order of population is:

Washington, Virginia, Pennsylvania and Texas

Part B: Z-score is the measure of how many standard deviations a mean is, i.e., how far from the mean a data is. To determine the z-score, use:

in which

x is sample, in this case, each state population mean;

μ is general population mean;

σ is general standard deviation;

Texas has a z-score of 1.52, which means, its population is 1.52 to the right of the general population mean. To determine the mean of Texas population:

i.e.:

x = 12522.22

Texas has a population of 125,22.22 millions.

Pennsylvania has a z-score of -0.15. This means its population is 0.15 to the left of the general population mean. So, population of Pennsylvania is:

x = 128.38

Pennsylvania has a population of 128.38 millions.

Therefore, from the smallest to the largest population:

Washington, Virginia, Pennsylvania and Texas.

529 and 531

step-by-step explanation: