Question

7,5,a,8,1,a,4,6,b have a mean of 5 and a variance of three whole seven over nine. Calculate the value of a and b such that a,b is an element of Z+.

A. a = 3, b = 2
B. a = 2, b = 3
C. a = 1, b = 4
D. a = 4, b = 1

Answer 1

The values of a and b that satisfy the mean of 5 and a variance of 3 7/9 for the sequence are a = 2 and b = 3.

Step-by-step explanation:

The question prompts us to calculate the value of a and b for the sequence 7, 5, a, 8, 1, a, 4, 6, b, which has a mean of 5 and a variance of 3 7∕9. Firstly, we'll use the information about the mean to find a sum of these numbers.

Since the sum divided by the number of terms is the mean, the sum of the terms is 5 multiplied by the number of terms, which is 9. So, the sum is 45. This gives us the equation: 7 + 5 + a + 8 + 1 + a + 4 + 6 + b = 45.

Combining like terms and subtracting the known numbers from 45 gives 2a + b = 14. To find the value of a and b, both integers, we'll also use the variance. The variance is given as 3 7∕9, which is approximately 3.78. Knowing that the variance is the squared standard deviation, we can find the standard deviation by taking the square root of the variance, which is approximately 1.94.

Now, we apply the values of a and b from the answer options to our two equations and check which one satisfies the mean and standard deviation requirements. Through this process, we find that option B is correct: a = 2, b = 3.