a. Obtain the cdf of X.b. What is P(X ≤ .5)?c. Using the cdf from (a), what is P(.25 < X ≤ .5)?d. What is the 75th percentile of the distribution? When we say that an individual's test score was at the 85th percentile of thepopulation, we mean that 85% of all population scores were below that score and15% were above. Let's define percentile formally.Let p be a number between 0 and 1. The (100p)th percentile of the distribu-tion of a continuous rv X, denoted by n(p), is defined byp = F(n(p)) = | f(y) dy.The median of a continuous distribution, denoted by u, is the 50th percentile.2. Let X denote the amount of space occupied by an item from Amazon placedin a 1-ft packing container. The pdf of X is[ 90x°(1 – x),f(x) =| 0,0 < x < 1otherwise

we have the pdf, f(x) = 90x8(1-x)= 90(x8-x9) for 0<x<1 we want to find, a. Obtain the cdf of…

Answered: a. Obtain the cdf of X. b. What is P(X…

a. Obtain the cdf of X. b. What is P(X ≤ .5)? c. Using the cdf from (a), what is P(.25 < X ≤ .5)? d. What is the 75th percentile of the distribution?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Related questions

Q: Calculate the median of the following distribution: CLASS FREQUENCY 10- 19 8 20-29 16 30-39 12 40-49…

Q: 4. (Proportion 5%) Supposing that X,,X,.,X,-N,(u,E) as an i.i.d with 2| is given. Determine the…

A: just find the mean vector and covariance matrix..............

Q: Q2 At a site, the clepith of the sand layer was measured for 10 points, and the results were as…

A: x 1.55 2.41 2.91 3.26 3.41 3.73 3.84 3.99 4.02 4.13 The mean is given by…

Q: There were 265 students who participated in a study collected at random. The distribution of…

A: Solution Given that The number of students n=265 The frequency table of X and Y is given Firstly…

Q: Which of the followings is NOT a correct statement about fourth-spread? O a. Conceptually, it is…

A: Fourth spread: Fourth spread is used to find the measure of variability of distribution. It is…

Q: The following data give the numbers of computer keyboards assembled at the Twentieth Century…

A: Formula for finding percentile rank is,

Q: For a negatively sloped distribution with Mode=18 and Median= 15, the mean is probably _____. What…

A: When the tail of the distribution is elongated to the right side, the shape of the distribution is…

Q: Table 3 X 0-9 10-19 20-29 30-39 40-49 f 3 4 1 1 1 c% 30% 70% 80% 90% 100%

Q: On average, a banana will last 6.5 days from the time it is purchased in the store to the time it is…

A: Given Population follows normal distribution μ= population mea of banana not rotten after bought…

Q: n psychology students took a standardized test. The scores are summarized in the Grouped Frequency…

A: Cumulative frequency means the sum of the frequencies of all the predecessor classes and the class…

Q: Here is the second data set. 74 57 91 90 81 69 39 96 69 3 a.What is the mean (x¯) of this data…

Q: What percentage of respondents have at least 6 pairs of shoes.B. 62% of all respondents that have…

A: In this context, X denotes the number of pairs of Shoes. The total number of students is 65. Given,…

Q: The amount of time that people spend at Grover Hot Springs is normally distributed with a mean of 78…

A: Note: According to our guidelines we can answer only three subparts and rest can be repost.

Q: For the histogram on the right determine whether the mean is greater than, less than, or…

A: Given that Histogram from which we have to identity the given data is skewed right or left or…

Q: Suppose that data for 57 randomly selected female high school athletes was collected on the maximum…

A: The mean is 79.6 and standard deviation is 13.9.

Q: For a sample with s = 9, a score of X = 67 corresponds to z = +1.00. What is the sample mean?

A: Given that: Sample standard deviation, s=9 Score, X=67 Z-score, z=1 To find: Value of sample mean

Q: 2. Let Y1, Y2, Ys be a random sample from N(0, 1), and let Y =EY. Let Y6 be another independent…

A: Given that Y1,Y2, . . ., Y5be a random sample from N0,1, and Y¯=15∑i=15Yi.

Q: Suppose you are constructing a Cl for a mean using the T-distribution and your sample size is 17.…

A: Degrees of freedom = n-1

Q: Which of the following statements is true of the usage of the median in statistics? It is the score…

A: We have given the following statement about the median in statistics.

Q: there are 26 students took the exam, the table below shows the frequency distribution s of their…

A: Given information: There are 26 students who took the exam. The frequency distribution of the…

Q: Compute the mean number of accidents per day. b.Compute the standard deviation. c. What is the…

A: We have given that the probability distribution for the number of traffic accidents daily in a small…

Q: Class (kg) Freq, f [80; 100) 4 [100; 120) [120; 140) 13 [140; 160) [160; 180) 5 40 The median is…

Q: In a distribution with o = 5, a z-score of z = +2.00 corresponds to a location that is 10 points…

A: From the provided information, Population standard deviation (σ) = 5 The z value = +2.00

Q: Here is part of a calculation in a spreadsheet working with sample data of x. Which statement is…

A: A population is the entire group that you want to draw about conclusions you draw about. A sample is…

Q: Hannah has a chicken coop with six hens. Let X represent the total number of eggs the hens lay on a…

A: Given that

Q: a. What is the distribution of X? X - N( 17 b. What is the distribution of ? ~ N( 17 0.8451✔ 08 08…

A: given data X~N(17,5)x¯~N(17,0.8451)

Q: faculty. Find the Quartiles of the distribution, then 30 students have marks qual to 65 or lower?…

A: Quartile: It divides the given observations into four equal parts. The first quartile is represented…

Q: 1. The incidence of cancer among phosphate mine workers and their exposure to radiation was…

A: Solution-: We want to perform χ2 test at 5% level of significance. Whether cancer incidence rates…

Q: Ise the accompanying data set to complete the following actions. .Find the quartiles. . Find the…

A: A quartile is a statistical term that describes a division of observations into four defined…

Q: A researcher interested in studying the presence of ageism (prejudice and discrimination toward…

A: The given frequency table is, Ageism Score Value (x) f73635647352413Higher scores indicate a higher…

Q: The distribution of observed scores (in percentages) in a Chemistry final examinations were as…

A: Option 1 is incorrect because it states that 25% of the students scored at least 89, but the…

Q: Compute the mean, median, and mode for the set of scores presented in the following frequency…

Q: The empirical distribution of some variable X is given by the following table. (x, are observed…

A: xi frequency(fi) cumulative frequency(cf) -12 5 5 -10 23 28 0 28 56 2 35 91 5 36 127 10…

Q: On average, a banana will last 6.8 days from the time it is purchased in the store to the time it is…

A: 1. Assume that μ is the population mean time to spoil if the banana is hung from the ceiling.

Q: Suppose the income of workers at your job follows a normal distribution. If you standardize their…

A: Given that. X~N( 0 , 1 ) μ=0 , ?=1 (for standard normal distribution)

Q: Find the value of Pif the mean of the following distribution is 12. I: 9 5 7 P 11 13 f: 6 8 15 9 8 4…

A: Consider the following distribution. Here, the objective is to find the value of P.

Q: A standard score (z-score) describes O How far a particular score is from the median. O How much…

A: The value of the z-score describes how many standard deviations, the data score is away from the…

Q: Find the highest possible value of x in the set: 8.2, 4.8, 7.7, 6.0, 5.5, 8.1, 7.3, 6.2, 9.2, 5.8,…

A: The formula for mean is given by : Mean = sum of all observationtotal number of observation…

Q: The table below shows the scores of a group of students on a 10-point quiz. Test Score Frequency 3 4…

Concept explainers

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!

Question

a. Obtain the cdf of X.

b. What is P(X ≤ .5)?

c. Using the cdf from (a), what is P(.25 < X ≤ .5)?

d. What is the 75th percentile of the distribution?

When we say that an individual's test score was at the 85th percentile of the
population, we mean that 85% of all population scores were below that score and
15% were above. Let's define percentile formally.
Let p be a number between 0 and 1. The (100p)th percentile of the distribu-
tion of a continuous rv X, denoted by n(p), is defined by
p = F(n(p)) = | f(y) dy.
The median of a continuous distribution, denoted by u, is the 50th percentile.
2. Let X denote the amount of space occupied by an item from Amazon placed
in a 1-ft packing container. The pdf of X is
[ 90x°(1 – x),
f(x) =
| 0,
0 < x < 1
otherwise

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Continuous Probability Distribution$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.

Similar questions

b. What proportion of 8- to 18-year-old Americans tronic devices? In symbols, p(5
Suppose your manager indicates that for a normally distributed data set you are analyzing, your company wants data points between z=−1.4 and z=1.4 standard deviations of the mean (or within 1.4 standard deviations of the mean). What percent of the data points will fall in that range?Answer: ____ percent (Enter a number between 0 and 100, not 0 and 1 and round to 2 decimal places)
Suppose we want to estimate p, the proportion of undergraduate students who cheat. One strategy to estimate p is to sample n undergraduate students and ask each one the following question directly: Have you ever cheated in answering one of your class requirements (quizzes, exams, assignments, projects, etc.? Let Y₁, Y₂,, Y, denote the "1/0" ("yes/no") responses. a. What is the distribution of Y₁, i=1,2,...,n? b. Based on your answer in (a), find the maximum likelihood estimator of p.
Please view attachment.
Using the appropriate table in textbook (Keller, Appendix B) or Excel, a. find z.05. Draw the distribution and locate the z-value (z.os) in the distribution. b. find-z.05. Draw the distribution and locate the z-value (-z.05) in the distribution. c. find t50,.01. Draw the distribution and locate the t-value (t50,.01) in the distribution. d. find-t50,.01. Draw the distribution and locate the t-value (-t50,.01) in the distribution. e. find X²0,.05. Draw the distribution and locate the x²-value (x²0,05) in the distribution. f. find F2,20,.05. Draw the distribution and locate the F-value (F2,20,.05) in the distribution.
Consider a t-distribution with 9 degrees of freedom. Find to.34.
Suppose that the speed at which cars go on the freeway is normally distributed with mean 80 mph and standard deviation 7 miles per hour. Let X be the speed for a randomly selected car. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N( 80 | 7 b. If one car is randomly chosen, find the probability that it is traveling more than 79 mph. c. If one of the cars is randomly chosen, find the probability that it is traveling between 82 and 87 mph. d. 71% of all cars travel at least how fast on the freeway? mph. Hint:
Find the highest possible value for x in the set 8.2, 7.7, 6, 4.8, 8.2, 5.8, 9.2, 7.3, 6.2, 8.1, 5.5, and x such that the mean of these scores is 7.
find the highest possible value for x in the set 8.2 , 7.7 , 6 , 4.8, 8.2 , 5.8 ,9.2, 7.3, 6.2, 8.1 , 5.5 and x such that the mean of this score is 7.
A student was analyzing a data set that was Normally distributed with a mean of . She calculated the z-score of a score z in the data set and looked up this value on a z-table (the same z-tables we have been using in class). The table gave a value of 0.4918 in this instance. Which of the following statements is true. O Any score in this data set has a 49.18% chance of being between 2 and z. O The score has a probability of 49.18. O The standard deviation of this data set is 0.4918 O The score x is 0.4918 standard deviations away from the mean.
* The table shows a frequency distribution of Mathematic session marks for 120 students in the second stage at engineering faculty. Find the Quartiles of the distribution, then 30 students have marks equal to 65 or lower? Choose either True or : False Mark: 30-39 40-49 50-59 60-69 70-79 80-89 90-100 Number of Students 1 3 11 21 43 32 9 False O True O
5A professor at a local. universily ok her students were hormally distnibuted with a mean of noted that the grade 78 and a Standard deviahon of 1o. a The profesor has informed us Hhat 16.6 percent of her Students recieved arades of A. What is the minium Score Ineeded to receive a grade of A? 1 12.1percent of her students failed the course and reci F3, What was the maximum s core those who recieve- among Cf 33 percent of the students recieve d grades B or bet A's and B's), What is the minimum Score of Those who a ber higher !