Answer:
.3192
Step-by-step explanation:
Understanding the question
Given the following
We are asked to find the probability that x ≤ 100
We can do so by finding the z score and then using a z-score chart to convert the z-score to probability.
Finding the z-score
We can find the z-score using the following formula
[tex]ZScore=\frac{x-\mu}{\sigma}[/tex]
We are given that μ = 108 , σ = 17 and x = 100
Thus, Z-Score = (100 - 108)/17 = -.47
Converting Z-Score to probability
Next, we look at a z-score chart.
If you view the attached image , the left side is the first digit that appears (.4) and the top is the second digit that appears (7). If you meet up at the two values, the probability is .3192
Hence, the probability that x is less than or equal to 100 is .3192
Important Note: When converting z-score to probability using the chart
If the problem is looking for the probability when x is less than a value (or when the shading is on the left side), you keep the probability as it is from the chart.
If the problem is looking for the probability when x is greater than a value (or when the shading is on the right side), you subtract the probability from 1.
