A crane operator wants the mean number of lifts per hour to be at least 9 over a 5 hour shift. In the first four hours she completed 8, 10, 7 and 9 lifts. S...
Question 1 Report
A crane operator wants the mean number of lifts per hour to be at least 9 over a 5 hour shift. In the first four hours she completed 8, 10, 7 and 9 lifts. She logs each hour's total on a whiteboard by the site entrance.
- Work out the least number of lifts she must complete in the fifth hour to achieve a mean of at least 9 lifts per hour (3)
- Write down the total number of lifts completed over the shift if she completes exactly this least number (1)
Answer Details
This question tests finding the least value needed to achieve a target mean, then finding the resulting total.
- To achieve a mean of at least 9 lifts per hour over 5 hours, the total must be at least \( 9\times5=45 \) lifts. The first four hours total \( 8+10+7+9=34 \), so the fifth hour needs at least \[ 45-34 = \] 11 lifts [3].
- If she completes exactly 11 lifts in the fifth hour, the total over the shift is \( 34+11 = \) 45 lifts [1].
"At least" turns the mean condition into an inequality on the total ( \(\text{total}\geq\text{target}\times\text{number of hours}\) ); the least fifth-hour value is the smallest number that makes this total condition true, found the same way as an exact target would be.
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