Question

5. The length of needles produced by a machine has standard deviation of 0.02 inches. Assuming that the distribution is normal, how large a sample is needed to determine with a precision of ±0.006 inches the mean length of the produced needles to 98% confidence?

Answer 1

Solution :

Given that,

standard deviation =s =   =0.02

Margin of error = E = 0.006

At 98% confidence level the z is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02/ 2 = 0.01

Z/2 = Z0.01 = 2.326 ( Using z table    )

sample size = n = [Z/2* / E] 2

n = ( 2.326*0.02 / 0.006 )2

n =60.11

Sample size = n =60

SOME TIME ANSWER SAYS 61 BUT ACCUARATE ANSWER IS 60