Answer to Question #2823 in Statistics and Probability for alyssa
Dr. Al Kali, an environmental chemist, measures the pH of numerous samples of water collected from a polluted lake. His data are normally distributed with a mean pH of 8.25 and a standard deviation of 0.35. What should Dr. Kali report as the margin of error for the 90% confidence interval for his data?
Let X ne the pH of numerous samples of water collected from a polluted lake. By assumption X has normal distribution N(8.25,0.35). Then Z=((X-8.25)/0.35) has normal distribution N(0,1).
Then margin of error is equal to δ = 0.35 * z, where z is such that P(-z< Z < z) = 0.9 If Φ is a c.d.f. for N(0,1), then z= - Φ-1 ((1-0.9)/2)= -Φ-1 (0.05)= 1.645