Ch 5, 6, 7, Questions 3

Question

The mass of a species of mouse commonly found in houses is normally distributed with a mean of 20.9 grams with a standard deviation of 0.12 grams.

Round your answers to 3 decimals.

a) 10% of all mice have a mass of less than____grams.

b) 30% of all mice have a mass of more than_____ grams.

Answer 1

The mass is normally distributed with mean, mu=20.9 grams, standard deviation, sigma=0.12 grams.

a) let 10% of all mice have a mass less than x1 grams.

We Need to find x1. The left tail area is 10%=0.10.

First method,

Using graphing calculator, pull up invnorm function,

Plug in left area =0.10, mean=20.9, standard deviation=0.12

The answer is 20.75 grams

Second method,

using z table, find the z value corresponding to left tail area 0.10 which is -1.28

The Z formula is, z=(x1-mu)/sigma. Plug in the values to get, -1.28=(x1-20.9)/.12.

Solve for x1 to get the value for x1=20.75 grams.

b)Let 30% of all mice have a mass more than x2.

The right area is 30% or 0.03.

Using graphing calculator the left area is (1-0.30)=0.70.

Pull up invnorm function, plug in area=0.70, mean=20.9, standard deviation=0.12.

The answer is 20.96 grams.

Using z table, the z score for right tail area =0.30 is +0.52

Plug in the values in the z score formula as above to get, 0.52=(x2-20.9)/0.12.

Solving for x2 will give the value 20.96 grams.