Introduction to Probability and Statistics
14th Edition
ISBN: 9781133103752
Author: Mendenhall, William
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 6, Problem 6.90SE
Notice the approximate normality of the histogram of the 5738 chest measurements.
a. The
b. Find the empirical estimate of the 95th percentile and compare with your answer in part a. (HINT: The 95th percentile will be in position
c. Find the 90th percentile of this distribution based on a normal curve with
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
30. An individual who has automobile insurance from a certain company is randomly selected. Let Y be the num- ber of moving violations for which the individual was cited during the last 3 years. The pmf of Y isy | 1 2 4 8 16p(y) | .05 .10 .35 .40 .10
a.Compute E(Y).b. Suppose an individual with Y violations incurs a surcharge of $100Y^2. Calculate the expected amount of the surcharge.
24. An insurance company offers its policyholders a num- ber of different premium payment options. For a ran- domly selected policyholder, let X = the number of months between successive payments. The cdf of X is as follows:
F(x)=0.00 : x < 10.30 : 1≤x<30.40 : 3≤ x < 40.45 : 4≤ x <60.60 : 6≤ x < 121.00 : 12≤ x
a. What is the pmf of X?b. Using just the cdf, compute P(3≤ X ≤6) and P(4≤ X).
59. At a certain gas station, 40% of the customers use regular gas (A1), 35% use plus gas (A2), and 25% use premium (A3). Of those customers using regular gas, only 30% fill their tanks (event B). Of those customers using plus, 60% fill their tanks, whereas of those using premium, 50% fill their tanks.a. What is the probability that the next customer will request plus gas and fill the tank (A2 B)?b. What is the probability that the next customer fills the tank?c. If the next customer fills the tank, what is the probability that regular gas is requested? Plus? Premium?
Chapter 6 Solutions
Introduction to Probability and Statistics
Ch. 6.3 - Consider a standard normal random variable with =0...Ch. 6.3 - Find these probabilities associated with the...Ch. 6.3 - Calculate the area under the standard normal curve...Ch. 6.3 - Calculate the area under the standard normal curve...Ch. 6.3 - Find the following probabilities for the standard...Ch. 6.3 - Find these probabilities for the standard normal...Ch. 6.3 - a. Find a z0 such that P(zz0)=.025 . b. Find a z0...Ch. 6.3 - Prob. 6.8ECh. 6.3 - Prob. 6.9ECh. 6.3 - a. Find a z0 such that P(z0zz0)=.90 . b. Find a z0...
Ch. 6.3 - Find the following percentiles for the standard...Ch. 6.3 - A normal random variable x has mean =10 and...Ch. 6.3 - Prob. 6.13ECh. 6.3 - Prob. 6.14ECh. 6.3 - A normal random variable x has mean 35 and...Ch. 6.3 - Prob. 6.16ECh. 6.3 - A normal random variable x has an unknown mean and...Ch. 6.3 - Hamburger Meat The meat department at a local...Ch. 6.3 - Human Heights Human heights are one of many...Ch. 6.3 - Christmas Trees The diameters of Douglas firs...Ch. 6.3 - Cerebral Blood Flow Cerebral blood flow (CBF) in...Ch. 6.3 - Braking Distances For a car traveling 30 miles per...Ch. 6.3 - Elevator Capacities Suppose that you must...Ch. 6.3 - Sunflowers An experimenter publishing in the...Ch. 6.3 - Prob. 6.26ECh. 6.3 - Prob. 6.27ECh. 6.3 - Prob. 6.28ECh. 6.3 - Prob. 6.30ECh. 6.3 - How Many Words? A publisher has discovered that...Ch. 6.3 - Prob. 6.32ECh. 6.4 - Consider a binomial random variable x with n=25...Ch. 6.4 - Prob. 6.36ECh. 6.4 - Prob. 6.37ECh. 6.4 - Let x be a binomial random variable with n=15 and...Ch. 6.4 - Let x be a binomial random variable with n=100 and...Ch. 6.4 - Prob. 6.40ECh. 6.4 - Prob. 6.41ECh. 6.4 - Prob. 6.42ECh. 6.4 - Prob. 6.43ECh. 6.4 - Prob. 6.44ECh. 6.4 - Prob. 6.45ECh. 6.4 - Prob. 6.46ECh. 6.4 - No Shows Airlines and hotels often grant...Ch. 6.4 - Prob. 6.49ECh. 6.4 - Pepsi’s Market Share Two of the biggest soft drink...Ch. 6.4 - Prob. 6.52ECh. 6.4 - Prob. 6.53ECh. 6 - Prob. 6.54SECh. 6 - Prob. 6.55SECh. 6 - Prob. 6.56SECh. 6 - Prob. 6.57SECh. 6 - a. Find a z0 such that P(z0zz0)=.95 . b. Find a z0...Ch. 6 - Prob. 6.59SECh. 6 - Let x be a binomial random variable with n=36 and...Ch. 6 - Prob. 6.61SECh. 6 - Prob. 6.62SECh. 6 - Prob. 6.63SECh. 6 - Prob. 6.64SECh. 6 - Prob. 6.65SECh. 6 - Prob. 6.66SECh. 6 - Prob. 6.67SECh. 6 - Prob. 6.68SECh. 6 - Prob. 6.69SECh. 6 - Used Cars A used-car dealership has found that the...Ch. 6 - Washers The life span of a type of automatic...Ch. 6 - Prob. 6.74SECh. 6 - Prob. 6.75SECh. 6 - Prob. 6.77SECh. 6 - Prob. 6.78SECh. 6 - Prob. 6.79SECh. 6 - Prob. 6.80SECh. 6 - No Shows An airline finds that 5% of the persons...Ch. 6 - Prob. 6.82SECh. 6 - Plant Genetics In Exercise 5.75, a cross between...Ch. 6 - Prob. 6.84SECh. 6 - Prob. 6.86SECh. 6 - Prob. 6.87SECh. 6 - Introvert or Extrovert? A psychological...Ch. 6 - Normal Distribution? The chest measurements for...Ch. 6 - Prob. 6.91SECh. 6 - Prob. 6.92SECh. 6 - Prob. 6.93SECh. 6 - Prob. 6.94SECh. 6 - Prob. 6.95SECh. 6 - Prob. 6.96SECh. 6 - Prob. 6.97SE
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Similar questions
- 38. Possible values of X, the number of components in a system submitted for repair that must be replaced, are 1, 2, 3, and 4 with corresponding probabilities .15, .35, .35, and .15, respectively. a. Calculate E(X) and then E(5 - X).b. Would the repair facility be better off charging a flat fee of $75 or else the amount $[150/(5 - X)]? [Note: It is not generally true that E(c/Y) = c/E(Y).]arrow_forward74. The proportions of blood phenotypes in the U.S. popula- tion are as follows:A B AB O .40 .11 .04 .45 Assuming that the phenotypes of two randomly selected individuals are independent of one another, what is the probability that both phenotypes are O? What is the probability that the phenotypes of two randomly selected individuals match?arrow_forward53. A certain shop repairs both audio and video compo- nents. Let A denote the event that the next component brought in for repair is an audio component, and let B be the event that the next component is a compact disc player (so the event B is contained in A). Suppose that P(A) = .6 and P(B) = .05. What is P(BA)?arrow_forward
- 26. A certain system can experience three different types of defects. Let A;(i = 1,2,3) denote the event that the sys- tem has a defect of type i. Suppose thatP(A1) = .12 P(A) = .07 P(A) = .05P(A, U A2) = .13P(A, U A3) = .14P(A2 U A3) = .10P(A, A2 A3) = .011Rshelfa. What is the probability that the system does not havea type 1 defect?b. What is the probability that the system has both type 1 and type 2 defects?c. What is the probability that the system has both type 1 and type 2 defects but not a type 3 defect? d. What is the probability that the system has at most two of these defects?arrow_forwardThe following are suggested designs for group sequential studies. Using PROCSEQDESIGN, provide the following for the design O’Brien Fleming and Pocock.• The critical boundary values for each analysis of the data• The expected sample sizes at each interim analysisAssume the standardized Z score method for calculating boundaries.Investigators are evaluating the success rate of a novel drug for treating a certain type ofbacterial wound infection. Since no existing treatment exists, they have planned a one-armstudy. They wish to test whether the success rate of the drug is better than 50%, whichthey have defined as the null success rate. Preliminary testing has estimated the successrate of the drug at 55%. The investigators are eager to get the drug into production andwould like to plan for 9 interim analyses (10 analyzes in total) of the data. Assume thesignificance level is 5% and power is 90%.Besides, draw a combined boundary plot (OBF, POC, and HP)arrow_forwardPlease provide the solution for the attached image in detailed.arrow_forward
- 20 km, because GISS Worksheet 10 Jesse runs a small business selling and delivering mealie meal to the spaza shops. He charges a fixed rate of R80, 00 for delivery and then R15, 50 for each packet of mealle meal he delivers. The table below helps him to calculate what to charge his customers. 10 20 30 40 50 Packets of mealie meal (m) Total costs in Rands 80 235 390 545 700 855 (c) 10.1. Define the following terms: 10.1.1. Independent Variables 10.1.2. Dependent Variables 10.2. 10.3. 10.4. 10.5. Determine the independent and dependent variables. Are the variables in this scenario discrete or continuous values? Explain What shape do you expect the graph to be? Why? Draw a graph on the graph provided to represent the information in the table above. TOTAL COST OF PACKETS OF MEALIE MEAL 900 800 700 600 COST (R) 500 400 300 200 100 0 10 20 30 40 60 NUMBER OF PACKETS OF MEALIE MEALarrow_forwardLet X be a random variable with support SX = {−3, 0.5, 3, −2.5, 3.5}. Part ofits probability mass function (PMF) is given bypX(−3) = 0.15, pX(−2.5) = 0.3, pX(3) = 0.2, pX(3.5) = 0.15.(a) Find pX(0.5).(b) Find the cumulative distribution function (CDF), FX(x), of X.1(c) Sketch the graph of FX(x).arrow_forwardA well-known company predominantly makes flat pack furniture for students. Variability with the automated machinery means the wood components are cut with a standard deviation in length of 0.45 mm. After they are cut the components are measured. If their length is more than 1.2 mm from the required length, the components are rejected. a) Calculate the percentage of components that get rejected. b) In a manufacturing run of 1000 units, how many are expected to be rejected? c) The company wishes to install more accurate equipment in order to reduce the rejection rate by one-half, using the same ±1.2mm rejection criterion. Calculate the maximum acceptable standard deviation of the new process.arrow_forward
- 5. Let X and Y be independent random variables and let the superscripts denote symmetrization (recall Sect. 3.6). Show that (X + Y) X+ys.arrow_forward8. Suppose that the moments of the random variable X are constant, that is, suppose that EX" =c for all n ≥ 1, for some constant c. Find the distribution of X.arrow_forward9. The concentration function of a random variable X is defined as Qx(h) = sup P(x ≤ X ≤x+h), h>0. Show that, if X and Y are independent random variables, then Qx+y (h) min{Qx(h). Qr (h)).arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Big Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt
Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
Big Ideas Math A Bridge To Success Algebra 1: Stu...
Algebra
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:Houghton Mifflin Harcourt
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
The Shape of Data: Distributions: Crash Course Statistics #7; Author: CrashCourse;https://www.youtube.com/watch?v=bPFNxD3Yg6U;License: Standard YouTube License, CC-BY
Shape, Center, and Spread - Module 20.2 (Part 1); Author: Mrmathblog;https://www.youtube.com/watch?v=COaid7O_Gag;License: Standard YouTube License, CC-BY
Shape, Center and Spread; Author: Emily Murdock;https://www.youtube.com/watch?v=_YyW0DSCzpM;License: Standard Youtube License