Randolph enters a restaurant and queues in line to order his favorite food. Suppose that the restaurant canserve his favorite food within X minutes after Randolph enters the restaurant. Suppose further thatRandolph eats his food within Y minutes after it is served, independent of the serving time.Let W = X + Y be the total amount of time that Randolph stays inside the restaurant. The PDFs of the randomvariables X and Y are shown below.fx(x)0.10.1fx (y)10fy(y) = 0.1e-0.1y152050What is the probability that Randolph stays within the restaurant for at most 18 minutes, i.e. P(W <18)?What is the expected value (in minutes) that Randolph stays within the restaurant?XY

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Answered: What is the probability that Randolph…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter1: Functions

Section1.EA: Extended Application Using Extrapolation To Predict Life Expectancy

Problem 5EA

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For the following table of data. x 1 2 3 4 5 6 7 8 9 10 y 0 0.5 1 2 2.5 3 3 4 4.5 5 a. draw a scatterplot. b. calculate the correlation coefficient. c. calculate the least squares line and graph it on the scatterplot. d. predict the y value when x is 11.
Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data are at or below for respiratory rates in breath per minute during the first 3 years of infancy are given by y=101.82411-0.0125995x+0.00013401x2 for awake infants and y=101.72858-0.0139928x+0.00017646x2 for sleeping infants, where x is the age in months. Source: Pediatrics. a. What is the domain for each function? b. For each respiratory rate, is the rate decreasing or increasing over the first 3 years of life? Hint: Is the graph of the quadratic in the exponent opening upward or downward? Where is the vertex? c. Verify your answer to part b using a graphing calculator. d. For a 1- year-old infant in the 95 th percentile, how much higher is the walking respiratory rate then the sleeping respiratory rate? e. f.

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What is the probability that Randolph stays within the restaurant for at most 18 minutes, i.e. P(W≤18)? What is the expected value (in minutes) that Randolph stays within the restaurant?