The mean cost to Metropolis of an insured hospitalized influenza patient is $5634 with a standard deviation of $1204 mg. Let us assume that the cost for any patient is independent from the cost of any other patient. In the coming influenza season, Metropolis expects 28900 insured hospitalized influenza patients. Suppose we look at the cost of each hospitalized influenza patient during the influenza season. Let M be the random variable representing the mean cost of all the 28900 insured hospitalized influenza patients. Let T = the random variable representing the total cost of the 28900 insured hospitalized influenza patients. a) What theorem will let us treat T and M as approximately normal random variables? Law of Large Numbers Convolution Theorem Chebychev's Theorem 301 Theorem Monte Carlo Theorem Central Limit Theorem b) What is the expected value of T? c) What is the standard deviation of T?

The mean cost to Metropolis of an insured hospitalized influenza patient is $5634 with a standard deviation of $1204 mg. Let us assume that the cost for any patient is independent from the cost of any other patient. In the coming influenza season, Metropolis expects 28900 insured hospitalized influenza patients. Suppose we look at the cost of each hospitalized influenza patient during the influenza season. Let M be the random variable representing the mean cost of all the 28900 insured hospitalized influenza patients. Let T = the random variable representing the total cost of the 28900 insured hospitalized influenza patients. a) What theorem will let us treat T and M as approximately normal random variables? Law of Large Numbers Convolution Theorem Chebychev's Theorem 301 Theorem Monte Carlo Theorem Central Limit Theorem b) What is the expected value of T? c) What is the standard deviation of T?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Q: A group of students (large group) took a test in mathematics and the final scores have a mean of 68…

A: Given information: The final scores in a mathematics test has Normal distribution. Considering the…

Q: 1) A company reports that the mean weight of yearling Angus steers is 1152 pounds with a standard…

A: We have given that X~N(mu, sigma^2) mu=1152 ,sigma =84 Z-score =(x-mu )/sigma Note :-According…

Q: The time spent on volunteer activities varies within a group of students. A particular group of…

A: Mean μ=2, standard deviations σ=3 , n=100 P( x̄>2.5)=?

Q: The breaking strengths of cables produced by a certain manufacturer have historically had a mean of…

A: From the provided information, Sample size (n) = 25 Sample mean (x̄) = 1932 Population standard…

Q: The population of weights of a particular fruit is normally distributed, with a mean of 265 grams…

A: Let X denote the population of weights of a particular fruit is normally distributed, with a mean of…

Q: Assume thAt scores on a standardized test are known to follow a bell shaped distribution with a mean…

A: L

Q: Alex's times for running a mile are Normally distributed with a mean time of 5.28 minutes and a…

Q: Suppose the birth weights of babies in a particular country are normally distributed with a mean of…

A: Answer:

Q: Which should be true if we use a large sample rather than a small one?

A: Here given , collect a representative random sample Here Sample size is large Here use central…

Q: Bob has a bulb factory that produces two types of bulbs: white light (x) and color light (y). It is…

Q: Two phone batteries are to be tested for how they last (i.e., lifetime). Phone battery A has a…

A: Phone battery A has a lifetime is normally distributed with mean 4.1 and standard deviation…

Q: When a there is a significant difference between two distributions, but the research fails to find…

A: The type II error is defined as the probability to fail to reject the null hypothesis, when the null…

Q: A particular fruit's weights are normally distributed, with a mean of 610 grams and a standard…

A: Assume that random variable X denotes a particular fruit's weight and follows normal distribution…

Q: In this problem we look at bags of potato chips. There are three weights we consider. Let us call…

A: Hi! Thank you for the question. As per the honor code, we are allowed to answer three sub-parts at a…

Q: Suppose a claim is made that the mean age of members of a golf club is 52 years. The population…

A: Given: n = 50 X = 56 years σ = 6 μ = 52 Formula Used: Test-statistic Z = X-μσn

Q: In a large section of a statistics class, the points for the final exam are normally distributed,…

A: Finding the lowest score that would qualify a student for an A grade:The points for the final exam…

Q: The critical value used in constructing a 95% confidence interval is ________. Question 16…

A: It is given that Sample mean = 6 Sample standard deviation = 2 Sample size = 8 Confidence interval…

Q: A researcher hypothesizes that the SUNY professors have a higher job satisfaction level than the…

A: State the hypotheses. That is, the population mean of the overall job satisfaction equals 28. That…

Q: The main purpose of inferential statistics is to know whether: random sampling error occurs. the…

A: Note: Hi there! Thank you for posting the question. As there are several independent questions,…

Q: In the year 2033, katy perry is a leading traveling nurse. Katy is interested in reducing the mean…

A: Population mean, μ=8.6 Sample size, n=46 Sample mean, x¯=8.1 Sample sd, s=1.2 α=0.05

Q: A person's blood glucose level and diabetes are closely related. Let � be a random variable measured…

A: Mean = 85 standard deviation=21 we know that Z-score: Z =[x-µ] /σ

Q: Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther.t Suppose a small…

A: In statistical inference, there are two types of estimation, 1) Point estimation and 2) Interval…

Q: Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther.t Suppose a small…

A: In statistical inference, there are two types of estimation, 1) Point estimation and 2) Interval…

Q: uppose a researcher wants to test if the average diastolic blood pressure in Irish-Americans is…

A: Given data,n=30Population mean μ=70sample mean is x=73sd is s=3test statistic t=?

Q: The Federal Bureau of Investigation (FBI) compiles data on crimes and crime rates and publishes the…

A: Let a variable X represents the violent crime distribution of the past year. Given that, the table…

Q: Carry your intermediate computations to three or more decimal places, and round your responses as…

A: Given that, Let μ be the population mean breaking strength of the cables. Population mean (μ) =…

Q: The breaking strengths of cables produced by a certain manufacturer have historically had a mean of…

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

The mean cost to Metropolis of an insured hospitalized influenza patient is $5634 with a standard deviation of $1204 mg. Let us assume that the cost for any patient is independent from the cost of any other patient. In the coming influenza season, Metropolis expects 28900 insured hospitalized influenza patients. Suppose we look at the cost of each hospitalized influenza patient during the influenza season. Let M be the random variable representing the mean cost of all the 28900 insured hospitalized influenza patients. Let T = the random variable representing the total cost of the 28900 insured hospitalized influenza patients.

a) What theorem will let us treat T and M as approximately normal random variables?
- Law of Large Numbers
- Convolution Theorem
- Chebychev’s Theorem
- 301 Theorem
- Monte Carlo Theorem
- Central Limit Theorem

b) What is the expected value of T? [Text Box]

c) What is the standard deviation of T? [Text Box]

d) If TK is T/2000 then what is the standard deviation of TK? [Text Box]

e) What is the approximate probability that T is greater than $163,000,000? [Text Box]

f) What is the standard deviation of M? [Text Box]

g) What is the approximate probability M is between 5630 and 5700? [Text Box]

h) Metropolis will set up an influenza contingency fund, F, so that there is only a 10% chance that the total cost of the 28900 hospitalized influenza patients will be greater than F? What is the desired F? [Text Box]

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

Trending now

This is a popular solution!

Step by step

Solved in 4 steps

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

Similar questions

To become an actuary, it is necessary to pass a series of 10 exams, including the most important one, an exam in probability and statistics. An insurance company wants to estimate the mean score on this exam for actuarial students who have enrolled in a special study program. They take a sample of 8 actuarial students in this program and find the mean of the sample is 6.0 with standard deviation of the sample 2.0. This sample will be used to calculate a 95% confidence interval for the mean score for actuarial students in the special study program. A 95% confidence interval for the mean score of actuarial students in the special program is from ________ to ________. Question 17 options: 1) 3.52 to 8.47 2) 4.69 to 7.31 3) 4.66 to 7.34 4) 4.33 to 7.67
In a large group of young couples, the stan- dard deviation of the husbands' ages is four years, and that of the wives' ages is three years. Let D denote the age difference within a couple. Under what circumstances might you expect to find that the standard deviation of age differences in the group is about 5 years? Instead you find it to be 2 years. One possibility is that the discrepancy is the result of random variability. Give another explanation.
A particular fruit's weights are normally distributed, with a mean of 419 grams and a standard deviation of 7 grams.If you pick 3 fruits at random, then 9% of the time, their mean weight will be greater than how many grams?Give your answer to the nearest gram.
Two normal distributions are compared. One has a mean of 10 and a standard deviation of 10. The second normal distribution has a mean of 10 and a standard deviation of 2. Which of the following is true? The dispersions of the distributions are different. The dispersions of the distributions are the same. The distributions are from two different families of distributions. The locations of the distributions are different.
A particular fruit's weights are normally distributed, with a mean of 483 grams and a standard deviation of 23 grams.If you pick 17 fruits at random, then 16% of the time, their mean weight will be greater than how many grams
The weights of 1,000 men in a certain town follow a normal distribution with a mean of 150 pounds and a standard deviation of 15 pounds. From the data, we can conclude that the number of men weighing more than 165 pounds is about , and the number of men weighing less than 135 pounds is about .
Suppose a researcher wants to test if the average diastolic blood pressure in Irish-Americans is different than the average diastolic blood pressure in the general population. Note that the average diastolic blood pressure in the general population is 70 mmHG. The researcher recruits 30 Irish-Americans into this particular study and then measures each of their diastolic blood pressures (mmHG). The population of this sample has a standard deviation equal to 3.0. What is the two-sided alternative hypothesis? (in words) Group of answer choices The mean is different than 70 The mean is different than 73 The mean is greater than 70 The mean is greater than 73
For a certain type of computers, the length of time between charges of the battery is normally distributed with a mean of 62 hours and a standard deviation of 11 hours. John owns one of these computers and wants to know the number of hours when the computer would have 12% of its battery life left. Sketch the region in question. Write a sentence describing what your answer represents about the problem's specefics.
A particular fruit's weights are normally distributed, with a mean of 636 grams and a standard deviation of 18 grams.If you pick 21 fruits at random, then 15% of the time, their mean weight will be greater than how many grams?
A particular fruit's weights are normally distributed, with a mean of 453 grams and a standard deviation of 28 grams. If you pick 10 fruits at random, then 12% of the time, their mean weight will be greater than how many grams?
A particular fruit's weights are normally distributed, with a mean of 689 grams and a standard deviation of 13 grams.If you pick 10 fruits at random, then 4% of the time, their mean weight will be greater than how many grams?Give your answer to the nearest gram.
The breaking strengths of cables produced by a certain manufacturer have historically had a mean of 1775 pounds and a standard deviation of 70 pounds. The Español company believes that, due to an improvement in the manufacturing process, the mean breaking strength, µ, of the cables is now greater than 1775 pounds. To see if this is the case, 16 newly manufactured cables are randomly chosen and tested, and their mean breaking strength is found to be 1806 pounds. Assume that the population is normally distributed. Can we support, at the 0.10 level of significance, the claim that the population mean breaking strength of the newly- manufactured cables is greater than 1775 pounds? Assume that the population standard deviation has not changed. Perform a one-tailed test. Then complete the parts below. 00 Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H,…