Question

select the correct answer from each drop - down menu.
according to data on the state of iowa, the amount of water used for cooking per household per month is normally distributed, with a standard deviation of 10.4 liters. a survey was carried out to estimate the population mean. with a sample size of 60 households, the mean quantity of water used for cooking was found to be 62.6 liters.
there is a 95% chance that the population mean lies between liters and liters.

Explanation:

Step1: Recall Confidence Interval Formula

For a 95% confidence interval of the population mean (when population standard deviation \(\sigma\) is known), the formula is \(\bar{x} \pm z_{\alpha/2} \frac{\sigma}{\sqrt{n}}\). Here, \(\bar{x} = 62.6\), \(\sigma = 10.4\), \(n = 60\), and \(z_{\alpha/2}\) for 95% confidence is 1.96.

Step2: Calculate Margin of Error (ME)

First, compute \(\frac{\sigma}{\sqrt{n}}=\frac{10.4}{\sqrt{60}}\approx\frac{10.4}{7.746}\approx1.343\). Then, \(ME = 1.96\times1.343\approx2.632\).

Step3: Find Lower and Upper Bounds

Lower bound: \(\bar{x}-ME = 62.6 - 2.632 = 59.968\approx60.0\) (or more precisely, calculate without rounding early). Upper bound: \(\bar{x}+ME = 62.6 + 2.632 = 65.232\approx65.2\) (or using exact calculation: \(\frac{10.4}{\sqrt{60}}\approx1.3426\), \(1.96\times1.3426\approx2.6315\), so lower: \(62.6 - 2.6315 = 59.9685\approx60.0\), upper: \(62.6 + 2.6315 = 65.2315\approx65.2\)).

Answer:

The 95% confidence interval for the population mean is between approximately 59.97 liters (or 60.0 liters) and 65.23 liters (or 65.2 liters). So the first drop - down should be around 59.97 (or 60.0) and the second around 65.23 (or 65.2). (If we calculate more precisely:
\(\frac{10.4}{\sqrt{60}}=\frac{10.4}{7.745966692}\approx1.3426\)
\(ME = 1.96\times1.3426\approx2.6315\)
Lower bound: \(62.6 - 2.6315 = 59.9685\)
Upper bound: \(62.6+2.6315 = 65.2315\))

So the values are approximately 59.97 (or 60.0) and 65.23 (or 65.2). If we use more decimal - free steps, the interval is \(\bar{x}\pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}=62.6\pm1.96\times\frac{10.4}{\sqrt{60}}\), which calculates to approximately (59.97, 65.23).