Question

Replacement times for stereos are normally distributed with a mean of 4.5 years and a standard deviation of 1.3 years. b. What percent of all of these stereos last no less than 5.0 years? c. The manufacturer wants to have a warranty so that only 10% of the stereos will have to be replaced free. How long should the warranty be on these stereos?

Answer 1

Solution :

Given that ,

b) P(x < 5.0)

= P[(x - $\mu$ ) / $\sigma$ < (5.0 - 4.5) / 1.3 ]

= P(z < 0.38)

Using z table,

= 0.6480

percent = 64.80%

c) Using standard normal table,

P(Z > z) = 10%

= 1 - P(Z < z) = 0.10  

= P(Z < z) = 1 - 0.10

= P(Z < 1.28 ) = 0.90  

z = 1.28

Using z-score formula,

x = z * $\sigma$ + $\mu$

x = 1.28 * 1.3 + 4.5

x = 6.16 years.