Suppose the distribution of the time $X$ (in hours) spent by students at a certain university on a particular project is gamma with parameters $\alpha=50$ and $\beta=2 .$ Because $\alpha$ is large, it can be shown that $X$ has approximately a normal distribution. Use this fact to compute the approximate probability that a randomly selected student spends at most 125 hours on the project.

Suppose the distribution of the time $X$ (in hours) spent by students at a certain university on a particular project is gamma with parameters $\alpha=50$ and $\beta=2 .$ Because $\alpha$ is large, it can be shown that $X$ has approximately a normal distribution. Use this fact to compute the approximate probability that a randomly selected student spends at most 125 hours on the project.

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: Components that are critical for the operation of electrical systems are replaced immediately upon…

A: 9. The given mean is 500, and standard deviation is 100. That is, μ=500,σ=100. A sample of 10…

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: Structures in a county need to be designed for earthquake loading. After a detailed seismic risk…

Q: 2Y 0 Show that has a x² distribution with 2 degrees of freedom.

A: Mean =θ ,

Q: 11 Components that are critical for the operation of electrical systems are replaced immediately…

A: 11. Let ∑x be the all components are in storage which follows normal distribution because the life…

Q: In a certain city, the daily consumption of water (in millions of liters) follows approximately a…

A: Probability = 0.1429Explanation:LetX : daily water consumption in millionsSoX∼Gamma(α=4,β=2)So PDF…

Q: e it takes me to wash the dishes is uniformly distributed between 5 minutes and 11 minut the…

A: Consider, X be the time taken for the washing the dishes.Thus, we have X~U(5, 11).Here Lower, i.e,…

Q: The Weibull distribution is widely used in statistical problems relating to aging of solid…

A: Given Alpha = 2.8 beta = 220 (a) What is the Probability at most 250 less than 250 more than 300 (b)…

Q: Suppose that the lifetime income of current graduates of UT is exponentially distributed. Of course,…

A: The mean of the exponential distribution is uniformly distributed between 0.8 million dollars and…

Q: Assume that the amounts of weight that male college students gain during their freshman year are…

A: a mean of μ=1.1 kg and a standard deviation of σ=4.5 kg.If 9 male college students are randomly…

Q: The weights of steers in a herd are distributed normally. The variance is 90,000 and the mean steer…

A: Let X be the weights of steers in a herd are distributed normally. And σ2=90,000 and μ=1400 lbs i.e.…

Q: Determine the probability that the minimum value in a random sample of size 5 from an exponential…

A: Required Probability = 0.9179 answer Calculations:

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: Suppose that the return for a particular investment is normally distributed with a population mean…

A: Solution-: Given: μ=100,σ=15 We want to find what score must a person have to qualify for this…

Q: The percent of persons (ages five and older) in each state who speak a language at home other than…

A: From the provided information, The probability distribution function of exponential distribution…

Q: Consider the ski gondola from Question 3. Suppose engineers decide to reduce the risk of an overload…

A: To find the probability that a group of 15 randomly selected skiers will overload the gondola, we…

Q: The Weibull distribution is widely used in statistical problems relating to aging of solid…

Q: There are many engineering properties which cannot be negative, and so cannot be modeled using a…

Q: The cost of all maintenance for a car during its first year is approximately exponentially…

A: f(x) = λe-λx , x >0 ====================== NOTE: As per the guidelines, I can solve only the…

Q: Two airplanes are flying in the same direction in adjacent parallel corridors. At time t = 0, the…

A: Here the given information is Two airplanes are flying in the same direction in adjacent parallel…

Q: The cost of all maintenance for a car during its first year is approximately exponentially…

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

Q: Assume that adults have IQ scores that are normally distributed with a mean of mμ=100 and a standard…

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

Video Video

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

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, probability and related others by exploring similar questions and additional content below.

Similar questions

Question 9 According to a study, the salaries of registered nurses are normally distributed with a mean of 55770 dollars and a standard deviation of 6955 dollars. Let X be the salary of a randomly selected registered nurse. 1. Describe the probability distribution of X and state its parameters and o: (μ: X Select an answer Select an answer B IZ XLIN Z 2. Find the probability that the salary of a randomly selected registered nurse is a. less than 71106 dollars. b. between 35101 and 48927 dollars. c. more than 71605 dollars. σ= (Round the answer to 4 decimal places) (Round the answer to 4 decimal places) (Round the answer to 4 decimal places) 3. Find the 55-th percentile for the salaries of registered nurses. decimal place) dollars (Round the answer to 1
Let Y be an exponential random variable with (unknown) mean 0.
The time to first failure X of the software of a medical linear acceleratormay be modeled normal with μ = 1100 hours and σ = 50 hours.
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) =
certain city, the daily consumption of water (in millions of liters) follows approximately a gamma distribution with rate = 0.5 and shape parameter=4. If the daily capacity of that city is 8 million liters of water, what is the probability that on any given day the water supply is more than the daily capacity? O 0.174 O 0.5665 O 0434 O 0.8264
The level of nitrogen oxides (NOX) and nonmethane organic gas (NMOG) in the exhaust over the useful life (150,000150,000 miles of driving) of cars of a particular model varies Normally with mean 8080 mg/mi and standard deviation 66 mg/mi. A company has 1616 cars of this model in its fleet. Using Table A, find the level ?L such that the probability that the average NOX + NMOG level ?¯x¯ for the fleet greater than ?L is only 0.030.03 ? (Enter your answer rounded to three decimal places. If you are using CrunchIt, adjust the default precision under Preferences as necessary. See the instructional video on how to adjust precision settings.)
Suppose the lifespan (in months) of a smartphone battery can be modeled as a continuous random variable with CDF F(x) = 1 − e-x/3 x ≥ 0 What is the probability that the battery lasts between 12 to 15 months?
I have problem in the question number #2, but the answer is with the result of question number #1
The Weibull distribution is widely used in statistical problems relating to aging of solid insulating materials subjected to aging and stress. Use this distribution as a model for time (in hours) to failure of solid insulating specimens subjected to AC voltage. The values of the parameters depend on the voltage and temperature; suppose a = 2.6 and B = 220. (a) What is the probability that a specimen's lifetime is at most 250? Less than 250? More than 300? (Round your answers to five decimal places.) at most 250 less than 250 more than 300 0.7520 0.7520 0.1065 x X X (b) What is the probability that a specimen's lifetime is between 100 and 250? (Round your answer to four decimal places.) 0.6312 (c) What value (in hr) is such that exactly 50% of all specimens have lifetimes exceeding that value? (Round your answer to three decimal places.) 191 Xhr
Use the Standard Normal Table or technology to find the z-score that corresponds to the following cumulative area. 0.9299 The cumulative area corresponds to the z-score of (Round to three decimal places as needed.) C
The Weibull distribution is widely used in statistical problems relating to aging of solid insulating materials subjected to aging and stress. Use this distribution as a model for time (in hours) to failure of solid insulating specimens subjected to AC voltage. The values of the parameters depend on the voltage and temperature; suppose a = 2.4 and ß = 220. (a) What is the probability that a specimen's lifetime is at most 250? Less than 250? More than 300? (Round your answers to five decimal places.) at most 250 less than 250 more than 300 0.74310 0.74310 0.12183 (b) What is the probability that a specimen's lifetime is between 100 and 250? (Round your answer to four decimal places.) 6032 (c) What value (in hr) is such that exactly 50% of all specimens have lifetimes exceeding that value? (Round your answer to three decimal places.) hr