Question

The amount of rainfall in January in a certain city is normally distributed with a mean of 3.3 inches and a standard deviation of 0.5 inches. Find the value of the 25th percentile, rounded to the nearest tenth.A. 0.8B. 3.0C. 3.6D. 3.1

Answer 1

Answer:

$B$

Explanation:

Here, we want to find the value of the 25th percentile

Mathematically:

The 25th percentile represents a probability of p = 0.25

The z-score of this value is -0.68 (it is left of the mean)

To get z-score, we use the following formula:

$\begin{gathered} z-\text{score = }\frac{x-\mu}{\sigma} \\ \mu\text{ = mean = 3.3} \\ \sigma=\text{ standard deviation = 0.5} \end{gathered}$

Substituting these values, we have it that:

$\begin{gathered} -0.68\text{ = }\frac{x-3.3}{0.5} \\ 0.5(-0.68)\text{ = x-3.3} \\ -0.34\text{ = x-3.3} \\ x\text{ = 3.3-0.34} \\ x\text{ = 2.96} \\ x\text{ = 3.0 (to the nearest tenth)} \end{gathered}$