Question

If the mean is 4.5 and the standard deviation is 1, what is the z-score for a data point of 6?

a) 1.5
b) 2.5
c) 3.5
d) 4.5

Answer 1

The z-score for a data point of 6 with a mean of 4.5 and a standard deviation of 1 is calculated to be 1.5, meaning the data point is 1.5 standard deviations above the mean.

Step-by-step explanation:

Calculating the Z-Score

To calculate the z-score for a data point in a set, you subtract the mean from the data point and then divide that result by the standard deviation. In this case, the z-score for a data point of 6, given a mean of 4.5 and a standard deviation of 1, is calculated as follows:

Z = (X - μ) / σ

Where:

• X = the data point in question
• μ = the mean of the data set
• σ = the standard deviation of the data set

So, for a data point of 6:

Z = (6 - 4.5) / 1

Z = 1.5 / 1

Z = 1.5

Therefore, the z-score is 1.5, which means the data point is 1.5 standard deviations above the mean. This aligns with option (b) 1.5.