contestada

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 8.4 years, and standard deviation of 0.6 years. The 4% of items with the shortest lifespan will last less than how many years?

Respuesta :

ajeigbeibraheem

Answer:

7.35 years

Step-by-step explanation:

Given that :

mean = 8.4

standard deviation = 0.6

From the negative z tables, the corresponding data for 0.04 = -1.75

So, using the z-score formula:

[tex]z = \dfrac{x - \mu}{\sigma}[/tex]

[tex]-1.75 = \dfrac{x - 8.4}{0.6}[/tex]

-1.75 × 0.6  = x - 8.4

- 1.05 = x - 8.4

x = -1.05 + 8.4

x =  7.35 years

the shortest lifespan will last less than 7.35 years

∴ the longest 4% will have lifespans longer than x = 8.4 + 1.75(0.6)

= 9.45 years