Sleep z Score A larger sample of 50 sleep times (hours) has a mean of 6.3 hours and a standard deviation of 1.4 hours. What is the z score for a sleep time of 5 hours?

The sample size of the sleep time is 50 (n).

The sample mean of the sleep time is 6.3 hours$\left(\overline{x}\right)$ .

The sample standard deviation is 1.4 hours (s).

The observed sleep time is 5 hours (x).

The z-score is the quotient of the difference between the raw score and the sample mean value, and the sample standard deviation.

Mathematically, it can be represented as$z=\frac{x-\overline{x}}{s}$

The difference between the observed sleep time and the sample mean time is obtained as follows:

$$\begin{gathered} x-\overline{x}=5-6.3 \\ =-1.3 \end{gathered}$$

Thus, the difference between the observed sleep time and the sample mean sleep time is –1.3 hours.

The quotient of the difference over the standard deviation measure is computed as follows.

$$\begin{gathered} z=\frac{x-\overline{x}}{s} \\ =\frac{5-6.3}{1.4} \\ =\frac{-1.3}{1.4} \\ =-0.9286 \end{gathered}$$

Thus, the calculated value of the z-score is –0.93.