A manufacturer sells lightbulbs under two different brands, BrightLite and EcoGlow. The lifespan, in days, of 500 BrightLite lightbulbs is summarised in the table below.
Lifespan of BrightLite Lightbulbs| Length of life (\(x\) days) | Number of bulbs |
|---|
| \(100<x\leq120\) | \(15\) |
| \(120<x\leq140\) | \(35\) |
| \(140<x\leq160\) | \(70\) |
| \(160<x\leq180\) | \(130\) |
| \(180<x\leq200\) | \(150\) |
| \(200<x\leq220\) | \(80\) |
| \(220<x\leq240\) | \(20\) |
Calculate an estimate of the mean lifespan of the BrightLite bulbs in days.[1]
Calculate an estimate of the standard deviation.[1]
The cumulative frequency curve shows the same information for the 500 BrightLite bulbs.
Use the curve to estimate the median lifespan of the bulbs.[1]
Use the curve to estimate the interquartile range of the lifespans.[2]
If a bulb is selected, find the probability that its lifespan is more than 160 days.[2]
90% of the bulbs have lifespan more than \(n\) days. Find \(n\).[1]
If two bulbs are randomly chosen, find the probability that one bulb has a lifespan of more than 160 days while the other has a lifespan of less than 140 days.[2]
The manufacturer also tested 500 EcoGlow bulbs. These bulbs had a smaller interquartile range than the BrightLite bulbs, but the same median lifespan. Describe how the cumulative frequency curve for the EcoGlow bulbs may differ from that of the BrightLite bulbs.[1]