# Math Help - Confidence Interval

1. ## Confidence Interval

Concentrations of atmospheric pollutants such as car-bon monoxide (CO) can be measured with a spectrophotometer. In a calibration test, 50 measurements were taken of a laboratory gas sample that is known to have a CO concentration of 70 parts per million ( ppm). A measurement is considered to be satisfactory if it is within 5 ppm of the true concentration. Of the 50 measurements, 37 were satisfactory.
a. Find a 95% confidence interval for the proportion of measurements made by this instrument that will be satisfactory.
b. How many measurements must be taken to specify the proportion of satisfactory measurements to within ± 0.10 with 95% confidence?

$\displaystyle p\pm Z_{1-\frac{\alpha }{2}}\times \sqrt{\frac{p(1-p)}{n}}}$