The length of needles produced by a machine has standard deviation of 0.01 inches. assuming that the distribution is normal, how large a sample is needed to determine with a precision of ±0.005 inches the mean length of the produced needles to 95% confidence?

Let X be the length of needle produced by machine. X follows Normal distribution with standard deviation σ=0.01

The margin of error ME = 0.005 and confidence interval is 95%

We have to find here sample size n from given information

The formula to find sample size when population standard deviation is known is

n =

where is critical z value for 95% confidence interval

We have confidence level, c=0.95

α = 1- c = 1-0.95 = 0.05

α/2 = 0.05 /2 = 0.025

z (0.025) is z score value for which probability below -z is 0.025 and above z is 0.025

Using z score table to get z critical value

z = -1.96

For confidence interval calculation we use positive z score value 1.96

The sample size will be then

n =

n = 15.3664

Rounding sample size to nearest integer n=15

a sample is needed to determine with a precision of ±0.005 inches the mean length of the produced needles to 95% confidence is 15

A. dividing 99 by 204 will tell you that 99 out of 204 of the people were females at the action movie.

Remember, you can do anything to an equation as long as you do it to both sidesminus 36 from both sides4.5(8-x)=66-2.5(3x+24)distribute36-4.5x=66-7.5x-60add like terms36-4.5x=-7.5x+6add 7.5x to both sides36+3x=6minus 36 from both sides3x=-30divide both sides by 3x=-10