Question

The lifetimes of ACME brand voltage regulators are normally distributed with
SD = 6 months. Suppose 5% of the alternators last more than 80 months.
What is the mean lifetime (in months) of this product?

Answer 1

Solution :

x = 80

standard deviation = = 6

Using standard normal table,

P(Z > z) = 5%

1 - P(Z < z) = 0.05

P(Z < z) = 1 - 0.05 = 0.95

P(Z < 1.645) = 0.95

z = 1.645

Using z-score formula,

x = z * +

= x - z * = 80 - 1.645 * 6 = 70.1

The mean lifetime (in months) of this product = 70.1 months