Use the ALEKS calculator to solve the following problems.
(a) Consider a $t$ distribution with 22 degrees of freedom. Compute $P(-1.52
Solution
Step 1 ：For part (a), we need to calculate the probability that a t-distributed random variable with 22 degrees of freedom falls between -1.52 and 1.52. This can be done by calculating the cumulative distribution function (CDF) at 1.52 and subtracting the CDF at -1.52.
Step 2 ：For part (b), we need to find the value of c such that the probability that a t-distributed random variable with 2 degrees of freedom is greater than or equal to c is 0.05. This can be done by calculating the inverse of the CDF (also known as the quantile function or the percent-point function) at 0.95 (since the total probability is 1, if the probability of being greater than c is 0.05, then the probability of being less than or equal to c is 0.95).
Step 3 ：Final Answer: For part (a), \(P(-1.52
Step 4 ：Final Answer: For part (b), \(c=\boxed{2.920}\) (rounded to three decimal places).
From Solvely APP
Solution
Step 1 ：For part (a), we need to calculate the probability that a t-distributed random variable with 22 degrees of freedom falls between -1.52 and 1.52. This can be done by calculating the cumulative distribution function (CDF) at 1.52 and subtracting the CDF at -1.52.
Step 2 ：For part (b), we need to find the value of c such that the probability that a t-distributed random variable with 2 degrees of freedom is greater than or equal to c is 0.05. This can be done by calculating the inverse of the CDF (also known as the quantile function or the percent-point function) at 0.95 (since the total probability is 1, if the probability of being greater than c is 0.05, then the probability of being less than or equal to c is 0.95).
Step 3 ：Final Answer: For part (a), \(P(-1.52 Step 4 ：Final Answer: For part (b), \(c=\boxed{2.920}\) (rounded to three decimal places).
