Question

An appliance dealer's website features the mean life expectancy values for major household appliances. A range hood's mean life expectancy is 14 years with a standard deviation of 2.5 years. Using the Empirical Rule, what is the probability that the range hood you buy would last more than 19 years

Answer 1

0.0548

Explanation:

Given that:

Mean (m) life expactancy of product = 14 years

Standard deviation (σ) = 2.5 years

Probability of buying a product which will last more than 18 years ;

x = 18 years

Using empirical formula:

Zscore = (x - mean) / standard deviation

Zscore = (18 - 14) / 2.5

Zscore = 4 /2.5

Zscore = 1.6

Hence ;

P(Z > 1.6)

P(Z > 1.6) = 1 - P(Z < 1.6)

P(Z < 1.6) = 0.9452

P(Z > 1.6) = 1 - 0.9452

P(Z > 1.6) = 0.0548

Hence, probability = 0.0548 OR 5.48%