Needed help with the last two Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 42 male firefighters are tested and that they have a plasma volume sample mean of $ \overline{x} = 37.5 \, \text{ml/kg} $ (milliliters plasma per kilogram body weight). Assume that $ \sigma = 8.00 \, \text{ml/kg} $ for the distribution of blood plasma.When finding a 99% confidence interval, what is the critical value for confidence level? (Give your answer to two decimal places.)$ z_c = 2.58 $(a) Find a 99% confidence interval for the population mean blood plasma volume in male firefighters. What is the margin of error? (Round your answers to two decimal places.)- lower limit: 34.32- upper limit: 40.68- margin of error: 3.18(b) What conditions are necessary for your calculations? (Select all that apply.)- [✔️] $ \sigma $ is known- [ ] $ \sigma $ is unknown- [✔️] $ n $ is large- [ ] the distribution of volumes is uniform- [ ] the distribution of volumes is normal(c) Interpret your results in the context of this problem.- [ ] We are 1% confident that the true average blood plasma volume in male firefighters falls within this interval.- [ ] The probability that this interval contains the true average blood plasma volume in male firefighters is 0.99.- [ ] The probability that this interval contains the true average blood plasma volume in male firefighters is 0.01.- [✔️] We are 99% confident that the true average blood plasma volume in male firefighters falls within this interval.(d) Which equation is used to find the sample size $ n $ for estimating $ \mu $ when $ \sigma $ is known?- [ ] $ n = \left( \frac{z_c \sigma}{E} \right)^2 $- [ ] $ n = \frac{z_c \sigma}{E} $- [ ] $ n = \left( \frac{z_c E}{\sigma} \right)^2 $- [

Given,To answer the last sub-parts.(c). The 99% confidence interval for the population mean interprets that we are confident that the average blood plasma volume in male firefighters falls in the interval.So, the last option - option (4) is the correct option.(d). Sample size - The formula for finding the sample size, when is known - option (4) is the correct option. All the remaining options are incorrect.The sample size necessary for a 99% confidence interval for a margin of error for the mean plasma volumes in firefighters - The sample size necessary for a 99% confidence interval for a margin of error for the mean plasma volumes in firefighters is 69. (c). Option 4 is the correct option.(d). Option 4, is the correct option.The sample size required is 69 male firefighters.