A track and field athlete recorded the following distances, in meters, for 5 long jump tri… — ACT

A track and field athlete recorded the following distances, in meters, for 5 long jump trials during a training session: $5.8$ , $6.2$ , $5.5$ , $6.5$ , and $6.0$ . The coach requires the athlete to achieve an overall mean distance of exactly $6.1$ meters across $6$ trials. What distance, in meters, must the athlete jump on the 6th trial to reach this target mean?

A
$0.5$
B
$1.1$
C
$6.1$
$6.6$ Answer
E
$7.2$

Answer

6.6

meters

To achieve a mean of

6.1

meters across

6

trials, the total combined distance must be

6 \times 6.1 = 36.6

meters. Summing the first 5 jump distances gives

5.8 + 6.2 + 5.5 + 6.5 + 6.0 = 30.0

meters. Subtracting this sum from the required total (

36.6 - 30.0

) yields

6.6

meters for the 6th trial.

Step-by-Step Solution

Calculate the total distance of the first 5 trials.

5.8 + 6.2 + 5.5 + 6.5 + 6.0 = 30.0

meters

Finding the total distance currently accumulated is necessary to determine how much more is needed.

Calculate the total required distance for all 6 trials to achieve the target mean.

6 \times 6.1 = 36.6

meters

The formula for the mean is

\text{Mean} = \frac{\text{Total Sum}}{\text{Number of Trials}}

, so

\text{Total Sum} = \text{Mean} \times \text{Number of Trials}

Subtract the current sum from the required total sum to find the required 6th jump distance.

36.6 - 30.0 = 6.6

meters

The difference between the required total distance and the current distance gives the necessary score on the final trial.

Key Concept

Target Mean with Missing Value

Estimated Time:1m 0s

Question

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