Determining The Standard Error, Or Standard Deviation Of The Sampling Mean Essay
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 = (6068.30)/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 = (6668.30)/1.075 = 2.14, and the associated probability is .0162.
5. 150138=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…

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