Solution
- We need to find the Z-score that corresponds to the value of x = 208. After this, we can proceed to find the probability of getting a population greater than this value using Z-distribution tables or a Z-score calculator.
- The Z-score formula is:
[tex]\begin{gathered} Z=\frac{X-\mu}{\frac{\sigma}{\sqrt{n}}} \\ where, \\ \sigma=\text{ The standard deviation} \\ \mu=\text{ The mean} \\ n=\text{ The number of data points in the sample} \end{gathered}[/tex]
- Thus, we can calculate the Z-score as follows:
[tex]\begin{gathered} X=208,\mu=196.2,\sigma=31.7,n=30 \\ \text{ Thus, we have:} \\ \\ Z=\frac{208-196.2}{\frac{31.7}{\sqrt{30}}} \\ \\ Z=2.03884 \end{gathered}[/tex]
- Now, we can apply the Z-score calculator to convert the Z-score to a probability as follows:
- Thus, the probability of getting a population greater than 208 is 0.020733
