A manufacturer knows that their items have a normally distributed lifespan, with a mean of 4 years, and standard deviation of 0.7 years.

Question

If you randomly purchase one item, what is the probability it will last longer than 5 years?

Answer 1

You need p (X>5)

On a TI-84

2nd VARS

normalcdf

lower = 5

upper = 1E99

mean = 4

standard deviation = 0.7

Hit paste twice

Answer 2

Compute the z-score:

 

z = (x-μ)/σ

 

where:

1. x is the data point = 5 years
2. μ is the mean of the data set = 4 years
3. σ is the standard deviation of the data set = 0.7 years

z=(5-4)/0.7 =1.43

 

Then look up the probability on a z score table (http://www.z-table.com/). This is the probability that the item will be than 4 years. The probability that it will last more than 4 years is 1 - the probability from the z-score table.

 P(Z > 1.43) = 1 - P(Z <1.43) = 1 - 0.9236 = 0.0764.