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.

Respuesta :

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.

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