What price do farmers get for their watermelon crops? In the third week of July, a random sample of 51 farming regions gave a sample mean of = $7.08 per 100 pounds of watermelon. Assume that is known to be $1.80 per 100 pounds. Find a 99% confidence interval for the population mean price (per 100 pounds) that farmers in this region get for their watermelon crop. Round your answer to the nearest cent.

Answer
a. $6.93 to $5.93 per 100 pounds
b. $6.89 to $7.27 per 100 pounds
c. $6.99 to $7.17 per 100 pounds
d. $6.83 to $7.33 per 100 pounds
e. $6.43 to $7.73 per 100 pounds

99% = mean ± 2.575 SEm

SEm = SD/√n

It would help if you proofread your questions before you posted them.

"Assume that is known to be $1.80 per 100 pounds."?

To find the 99% confidence interval for the population mean price, we can use the formula:

CI = sample mean ± (Z * (σ/√n))

where CI is the confidence interval, Z is the Z-score corresponding to the desired confidence level (99% in this case), σ is the known standard deviation, and n is the sample size.

Given that the sample mean is $7.08 per 100 pounds, the known standard deviation is $1.80 per 100 pounds, and the sample size is 51 farming regions, we can calculate the confidence interval.

First, we need to find the Z-score for the 99% confidence level. The Z-score can be found using a Z-table or a statistical calculator. For a 99% confidence level, the Z-score is approximately 2.576.

Next, we plug the values into the formula:

CI = $7.08 ± (2.576 * ($1.80/√51))

Calculating the expression within parentheses:

2.576 * ($1.80/√51) ≈ 0.543

Now, we can calculate the confidence interval:

CI = $7.08 ± 0.543

To find the upper and lower bounds of the confidence interval, we add and subtract the value of 0.543 from the sample mean:

Lower bound = $7.08 - 0.543 ≈ $6.54
Upper bound = $7.08 + 0.543 ≈ $7.62

Rounded to the nearest cent, the 99% confidence interval for the population mean price that farmers in this region get for their watermelon crop is approximately $6.54 to $7.62 per 100 pounds.

Among the answer choices given, the option that matches the calculated confidence interval is:

c. $6.99 to $7.17 per 100 pounds.