A normal resting heart rate for adults ranges from about 60 to 100 beats per minute (BPM). A doctor would like to estimate the average heart rate for one of his patients. The doctor instructs his patient to measure their resting heart rate twice a day for one week. The measurements are listed below. Assume that the distribution of all heart rate measurements of this patient is approximately normally distributed. 105 101 107 103 115 107 106 113 114 106 109 103 110 101 Determine the point estimate, and the sample standard deviation, s. Round the solutions to four decimal places, if necessary. I= 8 = Using a 99% confidence level, determine the margin of error, E, and a confidence interval for the average resting heart rate of this patient. Report the confidence interval using interval notation. Round solutions to two decimal places, if necessary. The margin of error is given by E A 99% confidence interval is given by

Given that z is a standard normal random variable, compute the following probabilities (to 4 decimals). P(-1.77<x<-1.07)

A mathematician stands on a beach with his dog at point A. He throws a tennis ball so that it hits the water at point B. The dog, wanting to get to the tennis ball as quickly as possible, runs along the straight beach line to point D and then swims from point D to point B to retrieve his ball. ASsume C is the point on the edge of the beach closest to the tennis ball (see figure). Complete parts (a) through (d) below. B. D C. a. Assume the dog runs at speed r and swims at speed s, where r>s and both are measured in meters/second. Also assume the lengths of BC, CD, and AC are x, y, and z, respectively. Find a function T(y) representing the total time it takes for the dog to get to the ball. T(y) =3

Solve 13. e)