Question

The shape of the distribution of the time required to get an oil change at a

10

​-minute

​oil-change facility is unknown.​ However, records indicate that the mean time is

11.6 minutes

​,

and the standard deviation is

4.3 minutes

What is the probability that a random sample of n =35 oil changes results in a sample mean time less than 10 ​minutes?

Answer 1

Solution :

Given that ,

mean = = 11.6 minutes

standard deviation = = 4.3 minutes

n = 35

=    = 11.6 minutes

= / n = 4.3 / 35 = 0.727

P( < 10) = P(( - ) / < (10 - 11.6) / 0.727)

= P(z < -2.20)

Using z table

= 0.0139