Solve the problem. Round to the nearest tenth unless indicated otherwise. The amount of rainfall in January in a certain city is normally distributed with a mean of 4.3 inches and a standard deviation of 0.3 inches. Find the value of the quartile .
To find the quartile in a normally distributed data set, you need to calculate the z-score for the quartile position and then use that z-score to find the corresponding value on the standard normal distribution table. The quartile position refers to the percentage of the data set that falls below it.
Since you want to find the quartile, which is the 25th percentile, the z-score for this position can be obtained from the standard normal distribution table. The z-score for the 25th percentile is -0.674.
To find the actual value of the quartile, you need to multiply the z-score by the standard deviation and add it to the mean:
Quartile = Mean + (Z-score * Standard Deviation)
= 4.3 + (-0.674 * 0.3)
Calculating this:
Quartile = 4.3 - 0.2022
= 4.0978
Rounding to the nearest tenth, the value of the quartile is approximately 4.1 inches of rainfall in January in the given city.
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability (.25) and its Z score. Insert Z and other data into equation below and calculate.
Z = (score-mean)/SD