### Analysis of Overbooked FlightsAirlines sometimes overbook flights. Suppose that for a plane with 50 seats, 55 passengers have tickets. Define the random variable \( Y \) as the number of ticketed passengers who actually show up for the flight. The probability mass function of \( Y \) appears in the accompanying table.| \( Y \) | 45 | 46 | 47 | 48 | 49 | 50 | 51 | 52 | 53 | 54 | 55 ||-----------|------|------|------|------|------|------|------|------|------|------|------|| \( p(y) \) | 0.05 | 0.10 | 0.12 | 0.14 | 0.25 | 0.17 | 0.06 | 0.03 | 0.05 | 0.01 | 0.02 |#### Calculations1. **Variance \( V(Y) \)**: Calculate and round your variance to four decimal places. 2. **Standard Deviation \( \sigma_Y \)**: Calculate and round your standard deviation to two decimal places.#### Probability DeterminationDetermine the probability that \( Y \) is within 1 standard deviation of its mean value.

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Use the data in the following table, which lists drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in the table. Drive-thru Restaurant A B C D Order Accurate 314 277 244 131 Order Not Accurate 33 51 34 18 If three different orders are selected, find the probability that they are all from restaurant D.
Suppose you choose four people at random from a Statistics class in which you know 20% of the students have an A average. Let X be the number of students in your sample who have an A average. Obtain the probability distribution for X and plot the probability histogram. X Probability 0 i N 3 A 0.45 0.4 0.35 0.3 i Probability histogram: 0.25 i MI 0.2 0.15- 0.1 0.05- 0 0 1 2 X Figure 1. 3 0.45 0.4 0.35 0.3 0.25 m 10 el 02 0.15 0.1 0.05 0 0 2 X Figure 2. 3 0.45 0.4 0.35- 0.3- 0.25 02- 0.15 0.1- 0.05 0 0 1 2 X Figure 3. 3
A census collected data on everyone that lived in a certain small town. The random variable X is the number of girls born to a randomly selected couple in that town who has four children. Its probability distribution is shown below. Complete parts a through c. X 4 O 0 P(X=x) 0.0857 2 0.3208 3 0.2415 0.2447 0.1073 i ne mean number of children in a family with four girls iS b. Obtain the standard deviation of the random variable. 0= 1.1209 (Round to four decimal places as needed.) c. Construct a probability histogram for the random variable; locate the mean; and show one-, two-, and three-standard-deviation intervals. Choose the correct histogram below. B. O C. D. Number of Girls Number of Girls Number of Girls Number of Girls 0.5- 0.5- 0.4- 0.3- 0.4- 0.5- 0.4- 0.3- 0.2- 0.1- 0.3- 0.2- 0.2- n 0.1- 0.1- 0 0012 0 1 2 3 4 01234 01234 01234 The mean is 2.0400. (Type an integer or decimal rounded to four decimal places as needed.) The one-standard-deviation interval is.. the…
Use the data in the following table, which lists drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in the table.. Drive-thru Restaurant C C 233 39 B 273 53 D 149 12 A Order Accurate 316 Order Not Accurate 38 If one order is selected, find the probability of getting food that is not from Restaurant A. The probability of getting food that is not from Restaurant A is (Round to three decimal places as needed.)
Use the data in the following table, which lists drive-thru order accuracy at popular fast food chairs. Assume that orders are randomly selected from theee inclued in the table. Drive-thru Restaurant o D Order Accurate Order Not Accurate 331 275 52 250 142 15 34 31 If three different orders are selected, find the probability that they are all from restaurant D. The probability is . (Round to four decimal places as needed) Check Answet.
Which of the following is a discrete random variable? O length of time spent watching movies volume of gas use in a household length of a bike number of butterflies in your backyard
K The following data represent the number of drivers involved in a fatal crash in 2016 in various light and weather conditions. Complete parts (a) through (c) below. Click the icon to view the data for fatal crashes in 2016. (a) Among fatal crashes in unknown weather conditions, what is the probability that a randomly selected fatal crash occurs when it is dawn/dusk? The probability that a randomly selected fatal crash in unknown weather conditions occurs when it is dawn/dusk is approximately. (Round to three decimal places as needed.) Data table Weather Daylight Dark, but Lighted 5875 497 51 54 255 Normal Rain Snow/Sleet Other Unknown 14,307 875 219 125 810 (...) Dark 8151 681 156 220 548 Dawn/Dusk Other 1183 87 40 71 65 8 2 9 133 X

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