In a statistics class, the mean and standard deviation of the scores obtained by students on a test were found to be 69 and 14, respectively. If the scores are normally distributed, what percentage of students scored below 74 ?
To determine the percentage of students who scored below 74 , we can use the properties of the normal distribution.
First, we need to calculate the Z-score for a score of 74 . The Z-score represents the number of standard deviations a particular value is from the mean.
The formula to calculate the Z-score is:
Where:
Plugging in the values:
Next, we need to find the cumulative probability associated with the Z-score of 0.3571 . This represents the percentage of values below 74 .
Using a standard normal distribution table or a calculator, we can find that the cumulative probability associated with a Z-score of 0.3571 is approximately 0.6449 .
To convert this probability to a percentage, we multiply it by 100 :
Therefore, approximately of students scored below 74 on the test.
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