Question

2. Quiz scores The scores on Ms. Martin's statistics

Answer 1

Using the concepts and properties of mean and standard deviation, it is found that:

• Each test score has to be multiplied by 4 and increased by 27.

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• The mean of a data-set is the sum of all values in the data-set divided by the number of values.
• If all values are increased by x, the mean will also be increased by x.
• If all values are multiplied by x, the mean will also be multiplied by x.

• The standard deviation of a data-set is the square root of the sum of the differences squared of each value and the mean, divided by the number of values.

• If all values are increased by x, the standard deviation remains constant.
• If all values are multiplied by x, the standard deviation is also multiplied by x.

In this problem:

• First, we multiply, to find the desired standard deviation, then we add, to find the desired mean.

• Standard deviation of 3 we want to be 12, thus, we multiply each test score by 4, as $\frac{12}{3} = 4$.
• Multiplying by 4, the standard deviation will already be 12, but the mean will be 48.
• We want a mean of 75, thus, we have to increase each test score by 27, as 75 - 48 = 27.

A similar problem is given at brainly.com/question/20640860