Question

e Vector Calculus 6t SI vector Calculus (9 x)OHw#5 x\e Modern Mathema× * probability-usinx -0 × × \ Welcome to the L \爽welcome to the LX Secure | https://uncc.instructure.com/courses/72445/assignments/352345?module-itemidz1221488 1, Sec 6.2 #14 2, Sec 6.3 #28, 30, 32, 42, 44 3, Sec 6.4 #48 4. We want to estimate the mean of a certain population. We know that the variance is 2. We get a random sample of size n from this population and estimate the mean μ by the sample mean Xn a) Use Chebyshev's inequality to give an upper bound on the probability that our estimator is more than.5 away from the mean, thus on r(X,-μ| > 0.5) b) Based on this inequality, what is the smallest value of n that we can choose to ensure that the probability is less than 0.1? Note: Part a) has been corrected. It previously said "is within .5 of" instead of "is more than.5 away from." The mathematical equation has not changed. Thank you to a student for pointing this out. Piazza Canvas to Banner Grade Submission Account Dashboar Courses Groups Previous Inbox

for Question 4 only parts a and b

Answer 1

a)

here std error =(varaince/n)^1/2 =(2/n)^1/2

from Chebychev's upper bound for P(|Xbar-$\mu$|>0.5) =1/k² ; where k =0.5/std error

hence upper bound =1/(0.5/(2/n)^1/2)² =8/n

b) for abvoe to be less than 0.1

8/n<0.1

n>8/0.1

n>80