Several studies have shown that the smiling times for an eight-week old baby follow a uniformdistribution between 0 and 23 seconds. i.e. any smiling time from 0 to 23 seconds is equally likely.For this problem, we will explore the distribution of the sample mean. Suppose you ask 500 peopleto collect a random sample of size n (i.e. each person will need to observe n independent smilingtimes). Let X; be the length, in seconds, of the th eight-week old baby's smile.(a) Theoretically, what are E(X) and Var(X)? Your answers can depend on the sample size n.Note that if X is uniformly distributed over (a, b), then the expectation and variance of X areVar(X) =E(X)=a+b2as you showed in the previous problem.and(b-a)²12'(b) The Matlab command that you can use to generate the uniform(a, b) random variables of sizen is unifrnd (a,b,n). For the kth person, where k € {1,2,..., 500}, use Matlab to generatea random sample of size n = 10, compute the sample mean and save it to the vector xbar1.You will end up with 500 sample means stored in the vector xbar1. What are the mean andvariance of the sample mean from the simulation? Verify that they are very close to theoreticalvalues from part (a). Turn in your Rcode as well.(c) Repeat tasks posed in part (b) for a sample size of n = 100. Please save your 500 sample meansto the vector xbar2.(d) Repeat tasks posed in part (b) for a sample size of n = 200. Please save your 500 sample meansto the vector xbar3.(e) Use the following Matlab code to plot side-by-side histograms from parts (b) to (d):subplot (1,3,1)hist (xbar1)subplot (1,3,2)hist (xbar2)subplot (1,3,3)hist (xbar3)Attach your plot to the homework. What do you notice on the variance of X when n increases?

(a) Since the smiling times of an eight-week old baby follow a uniform distribution…

Answered: ibution between 0 and 23 seconds. L.e.…

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...

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3. Given the following p.d.f.: f(x) = 3e-3x, where x > 0, find the Median. Show all work and simplify the Median value to lowest terms. %3D
2
9. The average weight of a Coastal male Grizzly Bear is approximately normal with E(x); =795 pounds and SD * (x) = 80 pounds. How likely is it to randomly select 64 Coastal male Grizzly Bears with a sample average weight of 810 pounds or more? Find the z-score for the problem above. Round the answer to the nearest ten-thousandth.
A population of N = 5 scores has a mean of µ = 8. If one score with a value of X = 4 is removed from the population, what is the value for the new mean? What is the mode for the population of scores shown in the frequency distribution table? X f 5 3 4 4 3 3 2 3 1 2 After every score in a sample of n = 5 is multiplied by 2, the mean is calculated and found to be M = 8. What was the mean of the original sample?
tion 9.32. Following is the distribution of marks obtained by 50 students in Mercantile Law. Calculate the median marks. If 60 per cent of the students pass this test, find the minimum marks obtained by a pass candidate,
NT #3 For each of the following, answer whether the distribution of X is necessarily normally distributed (YES) or not (NO), and briefly explain why. a) X = the sample mean age for random samples of size n = 50 from the population of New Yorkers of non-working age (defined as below 18 or above 64). b) X = the sample mean age for random samples of size n = 10 from the population of New Yorkers of non-working age (defined as below 18 or above 64). c) X = the sample mean age for random samples of size n = 10 from a population of individuals whose ages are known to be normally distributed.
llustration 19.18.. A sample study of the population of two districts gives that in district A the percentage of male population is 52% while this is the figure for the female percentage in the B district. If the size of the sample selected was in district A and B as 400 and 625 respectively, can both of these samples be taken to come from a population where the percentage of males and females is equal?
8
Question 2 What does the notation X-N(2,5) mean? A) X belongs to the set N, which contains the numbers 2 and 5. B X is normally distributed with mean = 2 and standard deviation = 5. с X is normally distributed with mean = 5 and standard deviation=2. X is a normally distributed variable than can equal 2 or 5.
We have a large dataset which we denote by D1, with values x1, x2, x3, ..., xN. Its mean is denoted by m. We create a new dataset D2 as follows: x1-m, x2-m, x3-m, ..., xN-m (that is, we subtract the mean from every data point). Then we create a new dataset by dividing every value in D2 by number 5. (so note that we said D2, not D1). What is the mean of D3? Group of answer choices 5 m m/5 m/ 25

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