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.
[tex]z=\frac{x-\mu}{\sigma}[/tex], where,
z = z-score,
x = Random sample score,
[tex]\mu[/tex] = Mean,
[tex]\sigma[/tex] = Standard deviation.
Upon substituting our given values in z-score formula, we will get:
[tex]z=\frac{5-7.5}{1.3}[/tex]
[tex]z=\frac{-2.5}{1.3}[/tex]
[tex]z=-1.923076923[/tex]
Upon rounding to two decimal places, we will get:
[tex]z\approx -1.92[/tex]
Therefore, you are [tex]-1.92[/tex] standard deviations from the mean or 1.92 standard deviation below mean.