Normal Distribution help please :)

[acroviak]

right.

im fairly good with normal distribution stuff, like working out mean, s.d, x, z etc etc...

but on this particular question....

its about lifetime of light bulbs. mean = 1700 hours, s.d 150 hours.

i have to make two observations on the distribution of lifetimes implied by this information

thanks for any help

[mfinney]

95% of all light bulbs will have a lifetime of 1700 hours +/- 294 hours (95% confidence interval is 1.96 x s.d)
99.7% of all light bulbs will have a lifetime of 1700 hours +/- 450 hours (99.7% confidence interval is 3 x s.d)

OR you could express this as
95% of all light bulbs will have a lifetime in the range 1406 to 1994 hours
and 99.7% of all light bulbs will have a lifetime in the range 1250 to 2150 hours

Does this help?

[mfinney]

Fraction Number of Standard
of Data Deviations from Mean

50.0% .674
68.3 1.000
90.0 1.645
95.0 1.960
95.4 2.000
98.0 2.326
99.0 2.576
99.7 3.000

[FeliciaT]

So the mean = 1700 hours and s.d = 150 hours

Which can be expressed as 95% of all lightbulbs will have a lifetime in the range 1406 to 1994 hours and second in a similar way, 99.7% will have a lifetime in the range 1250 to 2150 hours.

Once you've understood that, just use a regular chart mapping the values https://www.ztable.net/

How did we get this? As mfinney explained, one way to express your problem statement is 95% of lightbulbs with have 1700 +/- 294 hours of lifetime and 99.7% withh have a +/- 450 hours of lifetime. Hope you understand