Students tracked how many hours they slept a night for a month. The mean was 8.37 with a standard deviation 1.84. Assume that the distribution is normal. Find the probabilities (round to three decimal places): Probability a student gets between 7 and 9 hours of sleep. 

Students tracked how many hours they slept a night for a month. The mean was 8.37 with a standard deviation 1.84. Assume that the distribution is normal. Find the probabilities (round to three decimal places): Probability a student gets more than 9.3 hours of sleep

Draw a boxplot from the prior question. 

Students tracked how many hours they slept a night for a month. The mean was 8.37 with a standard deviation 1.84. Assume that the distribution is normal. Find the probabilities (round to three decimal places): Probability a student gets less than 6.75 hours of sleep. 

Use the following sample data set and solve for the standard deviation (round to two decimal places): 71, 76, 78, 77, 86, 82, 88, 83, 73, 77, 80, 72, 79, 81, 89, 82

Evaluate the following integral: (7 pts) Clearly show your work in the upload submission. (3 pts) Input your answer in the provided space below using the equation editor.

Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. (3 pts) Sketch the area enclosed by the given curves and draw a typical cylinder shell in the upload submission. (4 pts) Set up the integral for the volume based on your sketch and find the resulting volume in the upload submission. (2 pts) Input your answer with the correct unit in the provided space below. Type “pi” for “π” The exact volume is 

Use differentials (not Newton’s method) to estimate the number   to 5 decimal places. (7 pts) Clearly show your work in the upload submission. (2 pts) Enter your answers in the space below.  

Given:       Assume f is one-to-one.  (7 pts) Show your work in the upload submission. Input the final answer in the given space below. (1 pt) The is

Find the equation of the tangent line (in slope-intercept form) to the curve  at the point (π, 0) (6 pts) Clearly show your work in the upload submission. (2 pts) Enter your answers in the space provided below using the equation editor.