The daily demand x for water (in millions of gallons) in a town is a random variable with the probability density function (x) = xe 5, [0, ). -x/5, -хе (a) Find the mean and standard deviation of the demand. (Round your standard deviation to three decimal places.) | mean standard deviation (b) Find the probability that the demand is greater than 7 million gallons on a given day. (Round your answer to three decimal places.)

The daily demand x for water (in millions of gallons) in a town is a random variable with the probability density function (x) = xe 5, [0, ). -x/5, -хе (a) Find the mean and standard deviation of the demand. (Round your standard deviation to three decimal places.) | mean standard deviation (b) Find the probability that the demand is greater than 7 million gallons on a given day. (Round your answer to three decimal places.)

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

See similar textbooks

Related questions

Q: The failure time (T) of an electronic circuit board follows exponentially distribution with…

A: As per bartleby policy, I have solved only three sub parts. Please upload the remaining under…

Q: The time that it takes for the next train to come follows a Uniform distribution with f(x) =1/45…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: Let T be the time from birth until death (in years) of a randomly selected member of a population.…

A: T is the time from birth until death of a randomly selected member of a population.T has a Gamma…

Q: assign numerical values to coin flips: Heads is +1 and Tails is –1, each with probability 1⁄2. After…

A: Given that

Q: The graph shows the probability density function for a car brand that has a mean fuel efficiency of…

Q: The weights of steers in a herd are distributed normally. The standard deviation is 300lbs and the…

A: Given that. X~N( μ , ?) μ=1200 , ?=300 Z-score =( x - μ )/?

Q: The Random Variable X counts the number of students who passed a test in a class of 18 students. If…

A: Solution-: Given: n=18,p=0.457 We want to find P(X=2)=?

Q: Assume that adults have IQ scores that are normally distributed with a mean of u = 105 and a…

Q: A group of college students were surveyed to learn how many times they visited a dentist in the…

A: given data y p(y) y*p(y) 0 0.17 0 1 0.48 0.48 2 0.35 0.70 Σy*p(y) = 1.18

Q: The type of battery in Jim's laptop has a lifetime (in years) which follows a Weibull distribution…

A: Given The type of battery in Jim's laptop has a lifetime (in years) which follows a Weibull…

Q: Find the mean and variance for the probability distribution given by f(x)= 2x k(k+1)* -,x=1,2,3,...k

Q: Assume that a randomly selected subject is given a bone density test. Those test scores are normally…

A: Given, Mean = 0 Standard deviation = 1 The objective is to find the probability that a given score…

Q: The life of light bulbs is distributed normally. The variance of the lifetime is 225and the mean…

A: The probability of a bulb lasting for at most 540 hours is calculated below:

Q: The lifetime of an aquatic insect has an exponential disribution with parameter θ = 10 hrs. (i)…

A: The lifetime of an aquatic insect has an exponential disribution with parameter θ = 10 hrs.

Q: The lifespan(in years) of radio is an exponentially distributed random variable with parameter λ=…

A: The lifespan (in years) of radio is an exponentially distributed random variable with parameter λ=…

Q: What would be the mean and standard deviation of (X-μ)/(σ/√10) ? What would be the mean and…

A: The expression (X-μ)/(σ/√10) represents the standardization of a random variable X with mean μ and…

Q: The time to failure (in hours) for a laser in a cytometry machine is modeled by an exponential…

Q: The following table shows the returns of two types of investments, stocks (x) and bonds (y), under…

A: In the question text , we have been clearly asked : expected return from bonds? What is the risk…

Q: Let x be a random variable that represents white blood cell count per cubic milliliter of whole…

A: Standard normal distribution : Let x be the continuous random variable and it said to be follows…

Q: ople or more 18. The lifetime of a flashlight battery is normally distributed with a mean = 35.6 hr…

A: The lifetime of a flashlight battery is normally distributed with a mean = 35.6 hr with standard…

Q: eight where the probability density function for the weight of passenger luggage is increa al Rule…

Q: 2. Given r(t) = (2, e³t-3, 6t+2) with r(1) = (2, 1, 7) and r'(1) = (2,0, 5), find r(t).

A: The objective is to find r(t).

Concept explainers

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

The daily demand x for water (in millions of gallons) in a town is a random variable with the probability density function
(x) = xe 5, [0, ).
-x/5,
-хе
(a) Find the mean and standard deviation of the demand. (Round your standard deviation to three decimal places.)
|
mean
standard deviation
(b) Find the probability that the demand is greater than 7 million gallons on a given day. (Round your answer to three decimal places.)

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

Step 2

Step 3

Step 4

Step 5

Trending now

This is a popular solution!

Step by step

Solved in 5 steps with 13 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Point Estimation, Limit Theorems, Approximations, and Bounds$

Learn more about

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

Similar questions

Assume that adults have IQ scores that are normally distributed with a mean of mμ=100 and a standard deviation σ= 15. Find the probability that a randomly selected adult has an IQ less than 127. The probability that a randomly selected adult has an IQ less tha 127 is
The life of light bulbs is distributed normally. The variance of the lifetime is 900 and the mean lifetime of a bulb is 550 hours. Find the probability of a bulb lasting for at least 583 hours. Round your answer to four decimal places
The time that it takes for the next train to come follows a Uniform distribution with f(x) =1/45 where x goes between 4 and 49 minutes. Round answers to 4 decimal places when possible. Find the probability that the time will be at most 31 minutes. Find the probability that the time will be between 9 and 48 minutes
The distribution of the time until a Web site changes is important to Web crawlers that search engines use to maintain current information about Web sites. The distribution of the time until change (in days) of a Web site is approximated in the following table. Days until Probability Changes 1.5 0.05 0.25 0.35 0.20 0.15 3 4.5 7 Calculate the probability mass function of the days until change. *Answers should be in rational numbers with 2 decimal places.
Please solve in 30 minutes
The random variable X has an exponential distribution: X ~ Exponential(0.2). Find the following: (a) P(2 < X < 10) (b) P(X > 6) (c) Find the 70th percentile for X
A population has mean u=30 and standard deviation o=7. (A) Find the z-score for a population value of 9. (B) Find the z-score for a population value of 51. (C) What number has a z-score of -2.3
Today, the waves are crashing onto the beach every 5.1 seconds. The times from when a person arrives at the shoreline until a crashing wave is observed follows a Uniform distribution from 0 to 5.1 seconds. Round to 4 decimal places where possible. The probability that a person will be born between weeks 18 and 52 is P(18<x<52)P(18<x<52) = The probability that a person will be born after week 40 is P(x > 40) = P(x > 10 | x < 47) =
The variable W represents the weight of potatoes buns sold at the bakery. This variable is normally distributed with mean 90 g and standard deviation 6 g. (a) (i) Explain the meaning of S6 . (ii) Find the mean and standard deviation of S6 . (ii) Hence, Calculate P ( S6 2 560 g).
ansewr D and E only
The lifespans of light bulbs are known to follow an exponential distribution. The exponential distribution, often denoted exp(β), is characterized by a single mean parameter β. The exponential distribution has a unique property that its standard deviation is equal to its mean. Suppose you order 100 light bulbs known to each have lifespans (in years) distributed according to exp(4). What is the probability that the average lifespan of your 100 light bulbs exceeds 5 years? (Using R it possible)
Assume that the readings on the thermometers are normally distributed with a mean of 0∘ and a standard deviation of 1.00∘C. A thermometer is randomly selected and tested. Find the probability of each reading in degrees.(a) Between 0 and 1.64: (b) Between −2.89 and 0: (c) Between −1.78 and 1.03: (d) Less than −2.79: (e) Greater than 2.62: