The newest model of a car battery from a popular brand is supposed to have a lifetime of  60  months, but the lifetime varies slightly from battery to battery. It is known that the population of all lifetimes (in months) of this model of car battery is approximately normally distributed. You are a product reviewer who wants to estimate the standard deviation for this population with a random sample of  22  car batteries. Follow the steps below to construct a  99%  confidence interval for the population standard deviation of all lifetimes of this model of car battery. (If necessary, consult a list of formulas.) (a)Click on "Take Sample" to see the results from the random sample. Take Sample Number of carbatteries Sample mean Sample standard deviation Sample variance 22 57.16 0.38 0.1444   To find the confidence interval for the population standard deviation, first find the confidence interval for the population variance. Enter the values of the point estimate of the population variance, the sample size, the left critical value, and the right critical value you need for your  99%  confidence interval for the population variance. (Choose the correct critical values from the table of critical values provided.) When you are done, select "Compute".   Critical values Confidence level Left critical value Right critical value 99% =χ20.9958.034 =χ20.00541.401 95% =χ20.97510.283 =χ20.02535.479 90% =χ20.9511.591 =χ20.0532.671 Point estimate of the population variance:   Sample size:   Left critical value:   Right critical value:   Compute 99%  confidence interval for the population variance:   99%  confidence interval for the population standard deviation:         (b)Based on your sample, enter the values for the lower and upper limits to graph the  99%  confidence interval for the population standard deviation of all lifetimes of this model of car battery. Round the values to two decimal places.   99% confidence interval for the population standard deviation: 0.001.00