Write the equation as MOE = ±z*0.90(σ/√n). [Margin Of Error equals "plus or minus" (critical z-value for 90% confidence interval) times (population standard deviation) divided by (square root of sample size)].
Place values to obtain MOE = ±1.645(12.2 ounces ÷ √49) or ±2.867.
The normal distribution is used for a sample size greater than 30. A calculator program returns "proportion of area under the standard normal curve" as 0.4500150945 for 1.645, which doubles to 0.900030189 or the specified confidence interval of 90.0%.
With 90% confidence, one can then state that the population mean should fall between
(30 − 2.867) and (30 + 2.867) or 27.133 and 32.867.
