SAT College

Suppose that a variable
is normally distributed in a population and that the standard error of the mean of a sample of size = 155 is 1.35. Determine the population standard deviation,
. Give your answer precise to at least two decimal places.

Answers

Answer 1

The population standard deviation is approximately 16.78 when rounded to two decimal places.

To determine the population standard deviation (σ), we can use the formula relating the standard error of the mean (SE) and the sample size (n) to the population standard deviation:

σ = SE × √(n)

Given that the standard error of the mean (SE) is 1.35 and the sample size (n) is 155, we can substitute these values into the formula:

σ = 1.35 × √(155)

Calculating the square root of 155, we find:

σ = 1.35 × 12.4499

Multiplying 1.35 by 12.4499, we get:

σ ≈ 16.7823

It's important to note that the standard error of the mean (SE) is calculated as the standard deviation of the sample divided by the square root of the sample size:

SE = s / √(n)

The standard error of the mean (SE) is given as 1.35, so we directly used it in the formula to determine the population standard deviation.

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