Question

The Aluminum Association reports that the average American uses 56.8 pounds of aluminum in a year. A random sample of 51 households is monitored for one year to determine aluminum usage. If the population standard deviation of annual usage is 12.3 pounds, what is the probability that the sample mean will be more than 59 pounds _________.

a) 0.1003
b) 0.3997
c) 0.6003
d) 0.8997
e) 0.0003

Answer 1

A: 0.1003

Explanation:

We are given;

Population mean; μ = 56.8

Population size; n = 51

Population standard deviation; σ = 12.3

We want to find; P(x > 59)

We will use the z-score formula.

z = (x - μ)/(σ/√n)

z = (59 - 56.8)/(12.3/√51)

z = 1.28

From z-distribution table attached, we have; P(z < 1.28) = 0.8997

Thus;

P(z > 1.28) = 1 - 0.8997 = 0.1003