Answer:
• <em>The 90% inverval estimate of the mean amount of mercury in the population is </em><u>[0.420 ppm, 1.252 ppm]</u>.
Explanation:
<u>1) Data:</u>
• μ = 0.836 ppm
• σ = 0.253 ppm
• z = ?
• 90% confidence interval estimate of the mean = ?
<u />
<u>2) Finding Zo for Pr = 90%</u>
The symmetry of the standard normal distribution implies that, for the 90% confidence interval, 5% of the values (area) are above Zo and 5% are below = - Zo.
Using <em>technology</em> (statistic software) or a <em>table</em> of the standard normal probability, you find that for Pr ≥ 0.05 means Zo ≥ 1.6045.
And, by symmetry, Pr ≤ 0.05 means Zo ≤ -1.6045.
<u>3) Calculate the limits of the interval:</u>
<u />
• Formula: z = ( X - μ) / σ
• Upper limit: X = zσ + μ = 1.645 (0.253 ppm) + 0.836 ppm = 1.252 ppm.
• Lower limit: X = zσ + μ = -1.645 (0.253ppm) + 0.836 = 0.420 ppm.
Then, the 90% inverval estimate of the mean amount of mercury in the population is [0.420 ppm, 1.252 ppm] ← answer
