Question

1. Suppose the lifetimes of Hoover vacuum cleaners are normally distributed with an average life (μ) of 12 years and a population standard deviation (σ) of 1.4 years.

What proportion of Hoover vacuum cleaners will last 14 years or more?

2. Suppose the lifetimes of Hoover vacuum cleaners are normally distributed with an average life (μ) of 12 years and a population standard deviation (σ) of 1.4 years.

Calculate the 80th percentile.

3. Suppose the lifetimes of Hoover vacuum cleaners are normally distributed with an average life (μ) of 12 years and a population standard deviation (σ) of 1.4 years.

Calculate the 10th percentile.

4. Suppose the lifetimes of Hoover vacuum cleaners are normally distributed with an average life (μ) of 12 years and a population standard deviation (σ) of 1.4 years.

Calculate the 50th percentile.

5. Suppose the lifetimes of Hoover vacuum cleaners are normally distributed with an average life (μ) of 12 years and a population standard deviation (σ) of 1.4 years.

Calculate the 95th percentile.

Answer 1

1:

The z-score for X= 14 is

The proportion of Hoover vacuum cleaners will last 14 years or more is

Answer: 0.0764

2:

Here we need z-score that has 0.80 area to its left.

The z-score 0.84 has 0.80 area to its left. So required 80th percentile is

Answer: 13.176

3:

Here we need z-score that has 0.10 area to its left.

The z-score -1.28 has 0.10 area to its left. So required 10th percentile is

Answer: 10.208

4:

Here we need z-score that has 0.50 area to its left.

The z-score 0 has 0.50 area to its left. So required 50th percentile is

Answer: 12

5:

Here we need z-score that has 0.95 area to its left.

The z-score 1.645 has 0.95 area to its left. So required 95th percentile is

Answer: 14.303