# Determining The Standard Error, Or Standard Deviation Of The Sampling Mean Essay

1274 Words Jun 13th, 2016 6 Pages
Assignment
Ans 1.1
a) The standard error, or standard deviation of the sample mean, = population standard deviation/square root of sample size = \$10.75/14

b) z = (60-68.30)/10.75 = -0.77

from the z tables we see that the probability that z is less than -0.77 is .2206, so the probability that x is GREATER than 60 is 1-.2206 = .7794.

c) Now we are dealing with variation of the sample mean, so the standard error is 10.75/sqrt(100) = 1.075

Z = (66-68.30)/1.075 = -2.14, and the associated probability is .0162.
5. 150-138=12 = 1 standard deviation. By the empirical rule, we know that 68% of the data fall within 1 standard deviation of the mean, above and below. Since the normal distribution is symmetrical, 34% fall within 1 standard deviation below the mean (i.e. between 138 and 150). So a score of 138 is the equivalent of a z score of -1. Similarly, a score of 162 is the equivalent of a z score of 1.

By the Empirical Rule, approximately 95% of the data fall within 2 standard deviations above and below the mean, so that would be from 126 to 174.

Same principle as above, but this time it 's plus or minus 3 standard deviations, from 114 to 186.
Ans 1.2:
a) The standard error of the mean, also called the standard deviation of the mean, is a method used to estimate the standard deviation of a sampling distribution. To understand this, first we need to understand why a sampling distribution is required.
In statistics, point estimation involves the use of sample data to…