the ALEKS calculator to answer the following.
(a) Consider an $F$ distribution with 6 numerator degrees of freedom and 24 denominator degrees of freedom. Compute $P(0.83
Solution
Step 1 ：The problem is asking for two different calculations related to the F-distribution. The F-distribution is a type of statistical distribution that is often used in analysis of variance (ANOVA) and regression analysis.
Step 2 ：For part (a), we are asked to compute the probability that a random variable following an F-distribution with 6 numerator degrees of freedom and 24 denominator degrees of freedom falls between 0.83 and 0.98.
Step 3 ：For part (b), we are asked to find a value c such that the probability that a random variable following an F-distribution with 47 numerator degrees of freedom and 25 denominator degrees of freedom is greater than or equal to c is 0.05.
Step 4 ：For part (a), we can use the cumulative distribution function to compute the probabilities that the random variable is less than or equal to 0.83 and 0.98, and then subtract the former from the latter to get the probability that the random variable falls between these two values.
Step 5 ：For part (b), we can use the percent point function, also known as the inverse cumulative distribution function, to find the value c such that the probability that the random variable is less than or equal to c is 0.95 (since the probability that the random variable is greater than or equal to c is 0.05).
Step 6 ：For part (a), the probability of the random variable to fall between 0.83 and 0.98 under an F-distribution with 6 numerator degrees of freedom and 24 denominator degrees of freedom is approximately 0.098.
Step 7 ：For part (b), the value of c such that the probability that a random variable following an F-distribution with 47 numerator degrees of freedom and 25 denominator degrees of freedom is greater than or equal to c is 0.05 is approximately 1.85.
Step 8 ：Final Answer: For part (a), \(P(0.83
From Solvely APP
Solution
Step 1 ：The problem is asking for two different calculations related to the F-distribution. The F-distribution is a type of statistical distribution that is often used in analysis of variance (ANOVA) and regression analysis.
Step 2 ：For part (a), we are asked to compute the probability that a random variable following an F-distribution with 6 numerator degrees of freedom and 24 denominator degrees of freedom falls between 0.83 and 0.98.
Step 3 ：For part (b), we are asked to find a value c such that the probability that a random variable following an F-distribution with 47 numerator degrees of freedom and 25 denominator degrees of freedom is greater than or equal to c is 0.05.
Step 4 ：For part (a), we can use the cumulative distribution function to compute the probabilities that the random variable is less than or equal to 0.83 and 0.98, and then subtract the former from the latter to get the probability that the random variable falls between these two values.
Step 5 ：For part (b), we can use the percent point function, also known as the inverse cumulative distribution function, to find the value c such that the probability that the random variable is less than or equal to c is 0.95 (since the probability that the random variable is greater than or equal to c is 0.05).
Step 6 ：For part (a), the probability of the random variable to fall between 0.83 and 0.98 under an F-distribution with 6 numerator degrees of freedom and 24 denominator degrees of freedom is approximately 0.098.
Step 7 ：For part (b), the value of c such that the probability that a random variable following an F-distribution with 47 numerator degrees of freedom and 25 denominator degrees of freedom is greater than or equal to c is 0.05 is approximately 1.85.
Step 8 ：Final Answer: For part (a), \(P(0.83
