Question

The number of hours per day a college student spends on homework has a mean of 6 hours and a standard deviation of 1.25 hours. Yesterday she spent 3 hours on homework. How many standard deviations from the mean is​ that? Round your answer to two decimal places.

Answer 1

The student spent 3 hours on homework, which is 2.40 standard deviations below the mean, since the mean is 6 hours with a standard deviation of 1.25 hours.

Step-by-step explanation:

The number of hours per day a college student spends on homework has a mean of 6 hours and a standard deviation of 1.25 hours. To find out how many standard deviations from the mean the student is when she spent 3 hours on homework, we use the formula:

Z = (X - μ) / σ

Where Z is the number of standard deviations, X is the value in question (3 hours), μ is the mean (6 hours), and σ is the standard deviation (1.25 hours).

Plugging in the values, we get:

Z = (3 - 6) / 1.25
Z = -3 / 1.25
Z = -2.40

So, the student spent 3 hours on homework, which is 2.40 standard deviations below the mean. This represents a significant deviation from the average number of hours spent on homework.

Answer 2

-2.4

Step-by-step explanation:

To calculate how many standard deviations you are from the mean you use Z-score, which is exactly that.

The formula is:

`Z-score = (X-\mu)/(\sigma) \\Where \\X: Value \\\mu: Mean \\\sigma: Standard\ deviation \\`

Replacing the information given in the formula you get:

`Z-score = (3-6)/(1.25) = -2.4`

She is -2.4 standard deviations from the mean or 2.4 to the left