25 Assume that we want to construct a confidence interval. Do one of the following, asappropriate: (a) find the critical value ta/2. (b) find the critical value Zx/2, or (c) state thatneither the normal distribution nor the t distribution applies.The confidence level is 95%, o is not known, and the histogram of 58 player salaries (inthousands of dollars) of football players on a team is as shown.O A. ta/2=O B.(Round to two decimal places as needed.)FrequencyZa/2 =(Round to two decimal places as needed.)O C. Neither the normal distribution nor the t distribution applies.40-Select the correct choice below and, if necessary, fill in the answer box to complete your choice.30-20-10-04000 8000 12000 16000 20000Salary (thousands of dollars)

Let the random variable X be the salaries of football players on a team. The sample size n = 64 The population standard deviation σ is not known.Central limit theorem depicts that when the sample size is sufficiently large and has a finite variance, then the samples will be normally distributed and the samples mean will be approximately equal to the population mean. By observing the given plot, we can say that the distribution is positively skewed. and our sample size is n=64 is sufficiently large. So we can say that the given data follows the approximately normal distribution. Hence the given distribution follows the normality assumption and the population standard deviation is not known of the given distribution, in that case, the t-test is appropriate to use. Here t-test is appropriate for the distribution. The degrees of freedom are obtained as df=n-1=64-1=63 The confidence level is c=95% , The level of significance is obtained as: α=1-c=1-0.95=0.05 Use the Excel formula "=T.INV.2T(0.05,63)" to obtain the critical value. We get the approximate critical value for the two-tailed t-test at a 5% level of significance is 2.00. Option (A) is correct. t(α/2)=2.00 The remaining options are incorrect because normal distribution we use when the standard deviation is known. so options (B) and (C) are incorrect.