A lathe machine produces machine parts whose lengths are normally distributed with a standard deviation of 0.20 mm. A sample of 10 parts is found to have a mean of 16.35 mm. Based on this sample, what is the 95% confidence interval for the population mean ?

Question

A lathe machine produces machine parts whose lengths are normally distributed with a standard deviation of 0.20 mm. A sample of 10 parts is found to have a mean of 16.35 mm. Based on this sample, what is the 95% confidence interval for the population mean   ?

anonymous · Answer

@rational

rational · Answer

start by finding the "margin of error"

rational · Answer

whats the multipilier(Z*) value for 95% confidence interval ?

(look up in ur notes)

anonymous · Answer

.95

rational · Answer

there will be a multiplier value, look up ur notes once

rational · Answer

For 95% confidence interval, the multiplier value is `1.96` :

|dw:1432814569497:dw|

rational · Answer

therefore margin of error is
$$1.96*\frac{0.2}{\sqrt{10}} = ?$$

anonymous · Answer

I feel like I messed up

rational · Answer

messed up what

anonymous · Answer

.0153664 is what I got and that does not seem right to me

rational · Answer

work it again
use ur calculator

anonymous · Answer

calc says .1214314622

rational · Answer

looks good, round it to 0.12 maybe

rational · Answer

so the margin of error is 0.12

rational · Answer

subtract that from mean, what do u get ?

rational · Answer

16.35-0.12 = ?

anonymous · Answer

16.23

rational · Answer

yes thats the lower bound of confidence interval

rational · Answer

for upper bound simply add

16.35 + 0.12 = ?

anonymous · Answer

16.47

anonymous · Answer

16.22-16.47

rational · Answer

so the confidence interval is $$\large (16.23,~ 16.47)$$

anonymous · Answer

Tyty