A data set follows a normal distribution. The mean of the data set is 66 and the standard deviation of the data set is 1.2. Find a $z$-score for a data value of 64 from the set.
Round your answer to two decimal places.
Answer
Final Answer: The $z$-score for a data value of 64 from the set is \(\boxed{-1.67}\)
Step 1 ：A data set follows a normal distribution. The mean of the data set is 66 and the standard deviation of the data set is 1.2. We are asked to find a $z$-score for a data value of 64 from the set.
Step 2 ：The z-score is a measure of how many standard deviations an element is from the mean. It is calculated by subtracting the mean from the data value and then dividing by the standard deviation.
Step 3 ：In this case, the data value is 64, the mean is 66, and the standard deviation is 1.2. So, we can calculate the z-score using these values.
Step 4 ：Subtract the mean from the data value: \(64 - 66 = -2\)
Step 5 ：Divide the result by the standard deviation: \(-2 / 1.2 = -1.6666666666666667\)
Step 6 ：Round the result to two decimal places: \(-1.67\)
Step 7 ：Final Answer: The $z$-score for a data value of 64 from the set is \(\boxed{-1.67}\)
