Question

There is a​ 10% chance of the mean​ oil-change time being at or below the sample mean for which there is an area of 0.10 to the left under the normal curve with mu Subscript x overbar Baseline equals 16.2 and sigma Subscript x overbar Baseline equals 0.213 . Use technology to find this value for x overbar.

Answer 1

= 16.2, = 0.213

area under normal curve to the left of x is = 0.10

Here we want to find the 10th percentile to get the value of x

using TI-83 PLUS calculator we get value of as follows

we get

= 15.927

2)

Manually you can do it as

find the z-score related to area 0.10 using z table we get

z-score = -1.281

formula for z-score is

convert it for x as follows

X= ( z * ) +

X = ( -1.281 * 0.213 ) + 16.2

= 15.927