Question

Use the following information to determine your answers: The typical amount of sleep per night that adults get has a bell-shaped distribution with a mean of 7.5 hours and a standard deviation of 1.3 hours. Suppose last night you slept for 5 hours. How many standard deviations are you from the mean? Please round to the second decimal point.

Answer 1

We have been given that the typical amount of sleep per night that adults get has a bell-shaped distribution with a mean of 7.5 hours and a standard deviation of 1.3 hours. Suppose last night you slept for 5 hours.

We will use z-score formula to solve our given problem as z-score tells a data point is how many standard deviation from the mean.

$z=\frac{x-\mu}{\sigma}$, where,

z = z-score,

x = Random sample score,

$\mu$ = Mean,

$\sigma$ = Standard deviation.

Upon substituting our given values in z-score formula, we will get:

$z=\frac{5-7.5}{1.3}$

$z=\frac{-2.5}{1.3}$

$z=-1.923076923$

Upon rounding to two decimal places, we will get:

$z\approx -1.92$

Therefore, you are $-1.92$ standard deviations from the mean or 1.92 standard deviation below mean.