Moyu has access to a data set about the COVID-19 vaccine study. There are 120 patients in the study.

In the study, there are two types of vaccines A and B. The doctor rolls two dice and uses the following rule to assign the vaccine to each individual :

If the sum of the two dice is equal or greater than 8, the patient is assigned vaccine A. In the data, this is denoted as
Otherwise, the patient is assigned vaccine B. In the data, this individual is denoted by

Select all answers that are correct.

Question

Moyu has access to a data set about the COVID-19 vaccine study. There are 120 patients in the study.

In the study, there are two types of vaccines A and B. The doctor rolls two dice and uses the following rule to assign the vaccine to each individual :

If the sum of the two dice is equal or greater than 8, the patient is assigned vaccine A. In the data, this is denoted as 
Otherwise, the patient is assigned vaccine B. In the data, this individual is denoted by

Select all answers that are correct.

BlackTom AI · Accepted Answer

The problem describes a setup where two dice are rolled to assign vaccines, with a threshold at sum >= 8 to receive vaccine A; otherwise vaccine B. Let X(i) denote the indicator variable for receiving vaccine A on the i-th patient, so X(i) = 1 if the sum is ≥ 8 and X(i) = 0 otherwise. First, determine p, the probability that X(i) = 1. The sums that lead to A are 8, 9, 10, 11, and 12. The number of outcomes for each sum on two fair dice is: 8→5, 9→4, 10→3, 11→2, 12→1, totaling 5+4+3+2+1 = 15 outcomes out of 36. Therefore p = 15/36 = 5/12.

Option 1: The standard deviation of the sample mean of X(i) is approximately 0.045 (rounded to 3 decimals).
To evaluate this, recall that for a Bernoulli population with parameter p, the variance of a single X(i) is Var(X(i)) = p(1 − p). Here p = 5/12, so Var(X(i)) = (5/12)(7/12) = 35/144. The sample mean 
	n = 120 patients, so Var(

X̄) = Var(X(i)) / n = (35/144) / 120 = 35/17280 ≈ 0.002025. The standard deviation of the sample mean is SD(X̄) = sqrt(0.002025) ≈ 0.045. Rounding to three decimals gives 0.045. This line of reasoning shows the statement is correct.

Option 2: The variance of X(i) is 35/144.
As established above, Var(X(i)) = p(1 − p) with p = 5/12, so Var(X(i)) = (5/12)(7/12) = 35/144. This matches the stated value exactly, confirming this option is also correct.

In summary, both computed quantities align with the underlying Bernoulli model for X(i) with p = 5/12: the per-trial variance is 35/144, and the standard deviation of the sample mean for n = 120 is approximately 0.045 when expressed to three decimals.

ECMT5001 (ND) In Semester Homework 1.

查看解析

登录即可查看完整答案

类似问题

Random samples of size 49 are taken from a population that has 200 elements, a mean of 180, and a variance of 169. The distribution of the population is unknown. The mean and the standard error of the distribution of sample means are _____.

The expected value of equals the mean of the population from which the sample is drawn _____.

Suppose the weekly salaries of elementary school teachers in GA are normally distributed with a mean of $871 and a standard deviation of $82. What is the probability (P) that the mean salary of 40 elementary school teachers is higher than $953 a week?

The expected value of the sampling distribution of the sample mean is equal to

The mean expenditure at a tyre store is $85.00, with a population standard deviation of $9.00. From a random sample of 60 customers, what is the probability that the sample average sale per customer will be between $83 and $86?

Suppose that during any hour in a large department store, the average number of shoppers is 448, with a standard deviation of 21 shoppers. 2. What is the probability that a random sample of 49 different shopping hours will yield a sample mean between 441 and 446 shoppers?

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单