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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.

User Znq
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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=(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=(5-7.5)/(1.3)


z=(-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.

User MathiasJ
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