A set of N = 20 exam scores has a mean of m = 50. The instructor discovered that an error was made grading one exam, so 20 point
1 answer:
Answer:
The new mean for the exam scores is 51
Step-by-step explanation:
the mean can be calculated using the formula
mean of scores =
before the 20 points was added, the mean of the score was = 50.
Inserting this into the formula, we have:
50 =
from this, we can compute the sum total of the scores as
sum total = 50 × 20 = 1000
when the extra 20 marks is added, the sum of the entire scores will be changed to 1000 + 20 = 1020.
Hence the new mean will be computed as (New Sum total of scores / Number of students)
= = 51.
∴ The new mean of the scores is = 51
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In the equation above, b is the base, x is the exponent, and a is the answer. These same variables can be rearranged to be expressed as an exponential equation as followed:
Next, we need to understand basic logarithm rules.
1. When a value is raised to a power, we can move the exponent to the front of the logarithm. Example:
log(a^2) = 2log(a)
2. When two variables are multiplied together, we can add the logarithms of the individual variables together. Example:
log(ab) = log(a) + log(b)
3. When a variable is divided by another variable, we can subtract the logarithms of the individual variables. Example:
log(a/b) = log(a) - log(b)
Now we can use these rules to solve the problem.
We can rewrite the cube root as:
Now we can move the one-third to the front:
Now we can split up the logarithm:
Finally, we can move the exponent to the front of the log of A:
Distribute the one-third to get the answer:
The answer is (4).