In A Metal Fabrication Process Metal Rods Are Produced To A Specified Target Length Of 15 Ft.

Stats question help please?

EU (European Union) countries report that 46% of their labor force is female. The United Nations wants to determine if the percentage of females in the U.S. labor force is the same. Based on a sample of 500 employment records, representatives from the United States Department of Labor find that 240 are female. What is the margin of error for the 95% confidence interval of the proportion of females in the U.S. labor force?
Answer
0.089
0.036
0.044
0.056
0.022

In a metal fabrication process, metal rods are produced to a specified target length of 15 feet. Suppose that the lengths are normally distributed. A quality control specialist collects a random sample of 16 rods and finds the sample mean length to be 14.8 feet and a standard deviation of 0.65 feet. The 95% confidence interval for the true mean length of rods produced by this process is
Answer
14.345 to 15.255 ft.
13.912 to 15.688 ft.
14.454 to 15.146 ft.
13.834 to 15.766 ft.
14.544 to 15.056 ft.

A manufacturer of cheese filled ravioli supplies a pizza restaurant chain. Based on data collected from its automatic filling process, the amount of cheese inserted into the ravioli is normally distributed. To make sure that the automatic filling process is on target, quality control inspectors take a sample of 25 ravioli. The correct value of to construct a 99% confidence interval for the true mean amount of cheese filling is
Answer
2.797
1.318
2.060
1.711
2.787


Insurance companies track life expectancy information to assist in determining the cost of life insurance policies. ABI Insurance randomly sampled 100 recently paid policies and determined the average age of clients in this sample to be 77.7 years with a standard deviation of 3.6. The 90% confidence interval for the true mean age of its life insurance policy holders is
Answer
74.1 to 81.3 years
77.1 to 78.3 years
72.5 to 82.9 years
76.87 to 80.33 years
74.5 to 80 years

ABI Insurance wants to estimate the average life expectancy to within one year with 95% confidence. Previous studies have shown the mean age life expectancy of its clients to be 78.6 with a standard deviation of 4.48 years. How many randomly selected recently paid policies would they need to sample to achieve the desired level of accuracy?
Answer
78
121
83
98
54

Stats question help please?

I wish to answer ONLY one question
The following formulae will help you to answer the remaining questions. You can try yourself.

Confidence interval for the population parameter is
sample statistic +/- Margin of error
Margin of error = z or t critical value corresponding to the level of confidence*standard error of the sample statistic
standard error of mean = standard deviation / sqrt sample size
standard error of proportion = sqrt (p*(1-p)/n)

Answer to 4th question.
90% Confidence interval for the population mean (Mu) is
77.7 +/- 1.645*3.6/sqrt 100
77.7 +/- 0.6
The confidence interval is (77.7-0.6 , 77.7+0.6)
i.e. (77.1, 78.3)
CHOICE (b) is the answer