 Mathematics
The Sampling Distribution of the Sample Mean

### Question Description

A population has mean 1,542 and standard deviation 246.

Find the probability that the mean of a sample of size 100 will be within 100 units of the population mean, that is, between 1,442 and 1,642 The sample mean is the population mean: 1542.

The standard deviation of the sample mean (called the "standard error") is

population standard deviation / sqrt(sample size)

= 246 / sqrt(100)

= 24.6

So the probability that the sample mean will be outside 100 units is given by the normal distribution cdf at 1442, multiplied by two (since we can be in either the lower or upper tail of the distribution):

= 2x Norm.cdf( x, mean, sd )

= 2 x Norm.cdf( 1442, 1542, 24.6 )

4.80241 x10^-05

So the probability this sample mean will be within 100 units is:

1 - 4.80241 x10^-05

0.999951976 iainharlow (1041)
Boston College Anonymous
The tutor managed to follow the requirements for my assignment and helped me understand the concepts on it. Anonymous
The tutor was knowledgeable, will be using the service again. Anonymous
Awesome quality of the tutor. They were helpful and accommodating given my needs. Studypool 4.7 Trustpilot 4.5 Sitejabber 4.4 Brown University

1271 Tutors California Institute of Technology

2131 Tutors Carnegie Mellon University

982 Tutors Columbia University

1256 Tutors Dartmouth University

2113 Tutors Emory University

2279 Tutors Harvard University

599 Tutors Massachusetts Institute of Technology

2319 Tutors New York University

1645 Tutors Notre Dam University

1911 Tutors Oklahoma University

2122 Tutors Pennsylvania State University

932 Tutors Princeton University

1211 Tutors Stanford University

983 Tutors University of California

1282 Tutors Oxford University

123 Tutors Yale University

2325 Tutors