Question

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 q1. 1.1 4.2 4.1 4.5

Answer 1

We start by showing the position of the first quartile, Q1 on the normal distribution graph. Q1 happens at 25% of the data.

The graph is shown below

We are interested in the area to the left of Q1 and we know that the probability is 0.25

We can find out the value of z-score from the table as shown below 

The z-score when p=0.25 is 0.68

then changing this z-score into the actual value

$-0.68= \frac{X-4.3}{0.3}$
$-0.204=X-4.3$
$X=4.096$