Step 1 (a) Find a 90% confidence interval for the population mean price (per 100 pounds) that farmers in this region get for their watermelon crop. What is the margin of error? First, check that it is appropriate to use the normal distribution to estimate u. We have a simple random sample of prices for watermelon crops, and the sample size is n = 37. From the central limit theorem, this sample size is large enough for the x distribution to be approximately normal, so it is appropriate to use the normal distribution. We are also given o = 1.86, so we can compute a confidence interval for u. Recall that a confidence interval is a range of values from the sample mean, x, plus or minus the margin of error E. To compute E for the 90% confidence interval x - E to x + E, use the fact that Zo go = 1.645 from the table below. Confidence Interval Critical Values zz Level of Confidence c Critical Value zo 0.70, or 70% 1.04 0.75, or 75% 1.15 0.80, or 80% 1.28 0.85, or 85% 1.44 0.90, or 90% 1.645 0.95, or 95% 1.96 0.98, or 98% 2.33 0.99, or 99% 2.58 Apply the formula for margin of error and round the final answer to two decimal places. E = 20.90 n 1.86 V 37 Submit Skip (you cannot come back)