Final answer:
To find Shane's overall average, add the ratios of successful attempts at each bar height and divide by the total attempts: A = (2/3 + 4/6 + 1/4) / (3/3 + 6/6 + 4/4) = 19/36. Shane's overall average is approximately 0.528.
Step-by-step explanation:
To find Shane's overall average number of jumps completed in the high jump event, we can set up an equation that takes into account the number of successful jumps at each bar height compared to the total attempts. Since Shane completes 2 out of 3 jumps at the lowest bar, 4 out of 6 at the middle bar, and 1 out of 4 at the highest bar, we calculate the average by summing up the successful attempts and dividing by the total attempts.
The equation for the overall average (A) is:
A = (Number of successful jumps at all bars) / (Total number of attempts at all bars)
For Shane, this can be written as:
A = (2/3 + 4/6 + 1/4) / (3/3 + 6/6 + 4/4)
When we simplify the equation, we have:
A = (2/3 + 2/3 + 1/4) / (1 + 1 + 1)
A = (4/3 + 1/4) / 3
To combine the fractions 4/3 and 1/4, we find a common denominator, which is 12, and express the sum of the fractions over that common denominator:
A = ((4 × 4) / 12 + (1 × 3) / 12) / 3
A = (16/12 + 3/12) / 3
A = 19/12 / 3
A = 19/36
Converting this fraction to a decimal, we get Shane's overall average:
A ≈ 0.528 (rounded to three decimal places)
Therefore, Shane's overall average number of jumps completed is approximately 0.528.