Question

A simple random sample of 60 is drawn from a normally distributed population, and the mean is found to be 28, with a standard deviation of 5. Which of the following values is within the 95% confidence interval (z-score = 1. 96) for the population mean? Remember, the margin of error, ME, can be determined using the formula M E = StartFraction z times s Over StartRoot n EndRoot EndFraction. The value of 26, because it’s not greater than 26. 7 and less than 29. 3. The value of 27, because it’s greater than 26. 7 and less than 29. 3. The value of 32, because it’s greater than 23 and less than 33. The value of 34, because it’s not greater than 23 and less than 33.

Answer 1

For the simple random sample, drawn from a normally distributed population, value of 27, because it’s greater than 26. 7 and less than 29. 3.

What is normally distributed data?

Normally distributed data is the distribution of probability which is symmetric about the mean.

The mean of the data is the average value of the given data. The standard deviation of the data is the half of the difference of the highest value and mean of the data set.

Total number of sample is 60. The mean found to be 28, with a standard deviation of 5. The z-score is 1. 96.

The margin of error can be found out using the following formula as,'

$MOE=z\times\dfrac{\sigma}{\sqrt n}$

Put the values as,

$MOE=1.96\times\dfrac{5}{\sqrt 60}\\MOE=1.2652$

As, the mean of the sample is 28. Thus, the upper and lower limits are,

$UL=28+1.2652=292625\\UL=28-1.2652=26.7348$

Hence, For the simple random sample, drawn from a normally distributed population, value of 27, because it’s greater than 26. 7 and less than 29. 3.

Learn more about the normally distributed data here;

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