A survey of 30 random households living in Oakbrook Village collected their annual spending on fertilizers. The data are listed below:

234 149 416 215 245 171 1277 162 153 244 179 131 286 152 2167 286 232 196 140 98 206 96 241 236 143 15 575 165 373 136

1. Assume that we know the variance of fertilizer spending in Oakbrook Village is 160,000.

Construct an 88%-confidence-interval for the population mean of household fertilizer spending.

1. Now assume the variance of fertilizer spending is unknown. Construct a 95%-confidence-interval for the population mean of household fertilizer spending.
2. Do you think the 30 data points above are drawn from a normal distribution? Explain why or why not.
3. Let's maintain the assumption that the variance of fertilizer spending is known at 160,000. Suppose we want to construct a 95% confidence interval for the population mean of fertilizer spending. How many households at least should we survey to keep the margin of error below 100.