With a known population mean of 100, and a known standard error of the mean of 7.5, what is the probability of selecting at random a sample whose mean is 110 or greater?
I need help getting this started, thanks
Finding z-score with your data:
z = (110 - 100)/(7.5)
Finish the calculation. Check a z-table for your probability using the z-score (remember the question is asking "whose mean is 110 or greater" when looking at the table).
To calculate the probability of selecting a sample mean of 110 or greater, we can use the concept of the standard normal distribution.
The first step is to calculate the z-score, which measures the number of standard deviations a particular value is from the mean. The formula for calculating the z-score is:
z = (x - μ) / σ
Where:
- z is the z-score
- x is the value we want to find the probability for (in this case, 110)
- μ is the population mean (given as 100)
- σ is the standard error of the mean (given as 7.5)
Using these values, we can calculate the z-score:
z = (110 - 100) / 7.5 = 10 / 7.5 = 1.33
Once we have the z-score, we can find the probability associated with it using a standard normal distribution table or a statistical calculator. Since we are interested in the probability of selecting a sample mean of 110 or greater, we need to find the area under the curve to the right of the z-score.
Using the z-score of 1.33, we can look up the corresponding area under the curve in a standard normal distribution table or use a calculator. The area to the right of the z-score of 1.33 is approximately 0.0918 or 9.18%.
Therefore, the probability of randomly selecting a sample whose mean is 110 or greater is approximately 0.0918 or 9.18%.