In the field of accountancy, times spent studying by students in the week before professional exams follow a Normal distribution with a standard deviation of 8 hours. A random sample of 4 students was taken in order to estimate the mean study time for the population of all students.a) What is the probability that the sample mean exceeds the population mean by more than 2 hours?b) What is the probability that the sample mean differs from the population mean by more than 4 hours?c) Suppose that a second (independent) random sample of 10 students was taken. Without doing any calculations, state whether the probabilities in parts (a) and (b) would be higher, lower or the same for the second sample.

1. a) Probability that sample mean exceeds population mean by more than 2 hours is given by :…

Answered: In the field of accountancy, times…

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

Concept explainers

Question

In the field of accountancy, times spent studying by students in the week before professional exams follow a Normal distribution with a standard deviation of 8 hours. A random sample of 4 students was taken in order to estimate the mean study time for the population of all students.

a) What is the probability that the sample mean exceeds the population mean by more than 2 hours?
b) What is the probability that the sample mean differs from the population mean by more than 4 hours?
c) Suppose that a second (independent) random sample of 10 students was taken. Without doing any calculations, state whether the probabilities in parts (a) and (b) would be higher, lower or the same for the second sample.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Expert Solution

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Point Estimation, Limit Theorems, Approximations, and Bounds$

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