A given data set is normally distributed and has a mean of 50 and a standard deviation of 10. What value would lie 1 standard deviation to the left of the mean?
A. 40
B. 60
C. 50
D. 10
Answer (2)
The problem provides a mean of 50 and a standard deviation of 10.
To find the value 1 standard deviation to the left of the mean, subtract the standard deviation from the mean.
Perform the calculation: 50 − 10 = 40 .
The value 1 standard deviation to the left of the mean is 40 .
Explanation
Understand the problem We are given a normally distributed data set with a mean of 50 and a standard deviation of 10. We need to find the value that is 1 standard deviation to the left of the mean.
Set up the calculation To find the value 1 standard deviation to the left of the mean, we subtract the standard deviation from the mean. That is, we calculate: v a l u e = m e an − ( 1 × s t an d a r d \tdeviation )
Substitute the values Substituting the given values, we have: v a l u e = 50 − ( 1 × 10 )
Calculate the result Calculating the result: v a l u e = 50 − 10 = 40
State the final answer Therefore, the value that lies 1 standard deviation to the left of the mean is 40.
Examples
Understanding standard deviations is useful in many real-world scenarios. For example, in weather forecasting, knowing the average temperature and its standard deviation helps to predict the range of temperatures expected on a given day. In finance, standard deviation is used to measure the volatility of stock prices, helping investors assess risk. In education, it can help understand the spread of scores around the average grade in a class.
The value that lies 1 standard deviation to the left of the mean, which is 50 with a standard deviation of 10, is 40. Thus, the correct answer is A. 40.
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