Normal human blood pressure varies by age. The table below gives the average blood normal systolic blood pressure in mm Hg and corresponding age. Age(in year) 5 10 17 32 52 62 Blood Pressure 75 90 105 110 116 121 a Find the power law model that relates age and blood pressure. b. Use the model to estimate the normal systolic blood pressure for a person who is 21 years old.

A tank is leaking at an increasing rate as indicated by the data below. Use the table to answer the following questions. Time (hr) 8 1 2 50 150 3 4 5 6 7 240 290 410 550 600 720 Leakage (gal/hr) 0 30 An upper limit estimate for the amount of material leaked after 4 hours is 730 gal. (Simplify your answer.) A lower limit estimate for the amount of material leaked after 4 hours is (Simplify your answer.) gal.

A patient is classified as having gestational diabetes if their average glucose level is above 140 milligrams per deciliter (mg/dl) one hour after a sugary drink is ingested. Rebecca's doctor is concerned that she may suffer from gestational diabetes. There is variation both in the actual glucose level and in the blood test that measures the level. Rebecca's measured glucose level one hour after ingesting the sugary drink varies according to the Normal distribution with μ=140+5 mg/dl and σ=5+1 mg/dl. Using the Central Limit Theorem, determine the probability of Rebecca being diagnosed with gestational diabetes if her glucose level is measured: Once? n=5+2 times n=5+4 times Comment on the relationship between the probabilities observed in (a), (b), and (c). Explain, using concepts from lecture why this occurs and what it means in context.

When water flows across farmland, some soil is washed away, resulting in erosion. An experiment was conducted to investigate the effect of the rate of water flow (liters per second) on the amount of soil (kilograms) washed away. The data are given in the following table:   Flow rate 0.31 0.85 1.26 2.47 3.75 Eroded soil 0.82 1.95 2.18 3.01 6.07           Let xx represent the flow rate variable and yy represent the variable for soil eroded. Then   \bar x = 1.73, s_x = 1.38, \bar y = 2.81, s_y = 1.99xˉ=1.73,sx​=1.38,yˉ​=2.81,sy​=1.99   Use this to complete the following calculation of the correlation coefficient for these data.   r = \frac{1}{n-1}\left[\left(\frac{x_1 - \bar x}{s_x}\right)\left(\frac{y_1 - \bar y}{s_y}\right) + \left(\frac{x_2 - \bar x}{s_x}\right)\left(\frac{y_2 - \bar y}{s_y}\right) + \cdots + \left(\frac{x_n - \bar x}{s_x}\right)\left(\frac{y_n - \bar y}{s_y}\right)\right]r=n−11​[(sx​x1​−xˉ​)(sy​y1​−yˉ​​)+(sx​x2​−xˉ​)(sy​y2​−yˉ​​)+⋯+(sx​xn​−xˉ​)(sy​yn​−yˉ​​)]…