A logistics manager tracks the delivery time for shipments to a key customer. On average, the deliveries take 38 minutes with a standard deviation of 11 minutes. The delivery times are normally distributed. What is the expected value of the average delivery time for a random sample of 49 shipments?

Question

BlackTom AI · Accepted Answer

We start by identifying the given information: the population mean delivery time is 38 minutes and the standard deviation is 11 minutes, with shipments distributed normally.
Option 1: 38 minutes. This is the expected value of the sample mean when sampling 49 shipments, because the mean of the sampling distribution of the sample mean equals the population mean (mu). The sample size affects the spread (standard error) but not the center.
Option 2: 22.04 minutes. This value resembles a calculation involving the standard error, perhaps 11 / sqrt(49) = 11 / 7 ≈ 1.571, but 22.04 does not correspond to any correct interpretation of the sampling distribution’s mean or standard error. It incorrectly combines or squares terms, leading to an implausible mean.
Option 3: 1.86 minutes. This is far smaller than any reasonable sampling distribution standard error for this problem; it could arise if one mistakenly took the standard error and squared or misapplied unit conversions, but it has no basis as the mean of the sample means.
Option 4: 3.15 minutes. Similar to option 3, this value might appear as a questionable standard error or a miscalculation, but it does not represent the expected sample mean and misunderstands how the sampling distribution centers around the population mean.
In summary, the correct interpretation is that the average of 49 deliveries has the same expected value as the population mean, 38 minutes, while the other options misstate or miscalculate the central tendency or mix up standard error concepts with the mean.

A logistics manager tracks the delivery time for shipments to a key customer. On average, the deliveries take 38 minutes with a standard deviation of 11 minutes. The delivery times are normally distributed. What is the expected value of the average delivery time for a random sample of 49 shipments?

View Explanation

Log in for full answers

Similar Questions

A population, with a normal distribution, has a mean of 80 and a standard deviation of 7. For a sample of 49, the probability that the sample mean will be larger than 82 is

The St. Joe Company grows pine trees and the average annual increase in tree diameter is 3.1 inches (µ) with a population standard deviation of 0.5 inches. A random sample of n = 50 trees is collected. What is the probability of the sample mean being less the 2.9 inches?

位置15的问题 A population has a mean of 84 and a standard deviation of 12. A sample of 36 observations will be taken. The probability that the sample mean will be between 80.54 and 88.9 is 题库 1/1[input]. (Note: your answer should retain THREE decimal places.)

Whenever the population has a normal distribution, the sampling distribution of sample mean is a normal or near normal distribution

Given a population with a mean of 75 and a standard deviation of 12, the probability that the mean of a sample of 36 observations taken at random from this population exceeds 78 is:

Assume that the time needed by a worker to perform a maintenance operation is normally distributed, with a mean of 60 minutes and a standard deviation of 6 minutes. What is the probability that the average time needed by a sample of 5 workers to perform the maintenance is between 63 and 68 minutes?

A sample of size 50 is to be taken from a population whose mean and standard deviation are 52 and 20, respectively. The probability that the sample mean will be larger than 49 is:

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler