Question

The length of life of a certain type of automatic washer is approximately normally distributed with a
mean of 3.1 years and standard deviation of 1.2 years. If this type of washer is guaranteed for 1 year,
what fraction of original sales will require replacement?

Answer 1

4.01% of the original sales will require replacement after 1 year.

Z score

Z score is used to determine by how many standard deviations the raw score is above or below the mean. The z score is given by:

$z=\frac{x-\mu}{\sigma} \\\\where\ x=raw\ score,\mu=mean,\sigma=standard \ deviation$

Given that mean = 3.1, standard deviation = 1.2, hence:

For x < 1:

z = (1 - 3.1)/1.2 = -1.75

From the normal distribution table:

P(z <  -1.75) = 0.0401 = 4.01%

4.01% of the original sales will require replacement after 1 year.

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