Question

Solve the problem.

The amount of rainfall in January in a certain city isnormally
distributed with a mean of 3.4 inches and a standarddeviation of
0.5 inches. Find the value of the quartileQ1.

Answer 1

Q1 value is 3.0625 inches

Explanation:

Q1 is the 25th percentile, that is

P(z<z*)=0.25 where z* is the z-score of the 25th percentile.

Corresponding z* is -0.675.

z* can also be calculated using the equation

z=
`(X-M)/(s)` where

• X is the 25th percentile(Q1) value

• M is the mean rainfall in January in the city (3.4 inches)

• s is the standard deviation (0.5 inches)

Solving the equation for X, we have X=-0.675×0.5+3.4 =3.0625 inches