Multiple Choice Question

Question

Luther is being tested on his typing skills. His grade will be based on the mean of his typing speeds from six trials. His rate, in words per minute, for the first five trials were 44, 50, 46, 48, and 42.

At what speed will he need to type the sixth trial to have a mean speed of 48 words per minute?

Answer 1

To find out the speed Luther needs to type in his sixth trial to achieve a mean speed of 48 words per minute, we can use the formula for the mean:

\[ \text{Mean} = \frac{\text{Sum of all trials}}{\text{Number of trials}} \]

He wants the mean speed to be 48 words per minute over 6 trials. This means we can set up the equation:

\[ 48 = \frac{S}{6} \]

where \(S\) is the sum of all speeds over the 6 trials.

To find \(S\), we multiply both sides by 6:

\[ S = 48 \times 6 = 288 \]

Next, we need to calculate the sum of his first five trials:

\[ 44 + 50 + 46 + 48 + 42 = 230 \]

Now, let \(x\) be the speed of the sixth trial. We can set up the equation:

\[ 230 + x = 288 \]

To solve for \(x\), subtract 230 from both sides:

\[ x = 288 - 230 = 58 \]

Thus, Luther will need to type at a speed of 58 words per minute in his sixth trial to achieve a mean speed of 48 words per minute.