a set of data items is normally distributed with a mean of 40 and a standard deviation of 3. convert 46 to a…
a set of data items is normally distributed with a mean of 40 and a standard deviation of 3. convert 46 to a z - score.
Answer
Explanation:
Step1: Recall the z - score formula
The formula for the z - score is (z=\frac{x-\mu}{\sigma}), where (x) is the data item, (\mu) is the mean, and (\sigma) is the standard deviation.
Step2: Substitute the given values into the formula
Given (x = 46), (\mu=40), and (\sigma = 3). Then (z=\frac{46 - 40}{3}).
Step3: Calculate the numerator
(46-40=6). So the formula becomes (z=\frac{6}{3}).
Step4: Calculate the z - score
(\frac{6}{3}=2).
Answer:
(2)