Mathematics Higher Level Robert Joinson

©Sumbooks2002Higher Level76. Cumulative Frequency (2)1. ‘Shiny’ long life bulbs are guaranteed to last at least 7,500 hours before breaking down. Inorder to make this guarantee, ‘Shiny’ did trials on 300 bulbs. These are the results:Life of bulb (hrs)5000 to59996000 to69997000 to79998000 to89999000 to999910,000 to11,000Frequency of breakdown 5 20 42 95 80 58a) Make a cumulative frequency table for this data.b) From the table, draw a cumulative frequency diagram. Use a scale of 2cm to 1000 hourson the horizontal axis and 2cm to 40 bulbs on the vertical axis.c) From the graph, estimate the percentage of bulbs that fulfil the guarantee.2. A flying school gives 1 hour lessons. Some of that time is spent on the ground havinginstruction and some in the air. The time spent in the air for 100 lessons were as follows.Time spentin the air20-30mins30-35mins35-40mins40-45mins45-50mins50-55minsFrequency 6 10 12 34 23 15a) Make a cumulative frequency table for this data. From the table, draw a cumulativefrequency diagram. Use a scale of 1cm to 2 mins horizontally and 1cm to 5 peoplevertically.c) From the diagram, estimate the median and interquartile range of the data.3. The times that trains arrive at a station are recorded by the station staff. They record whethera train is early or late and by how much. The table below shows their data for one day.Timing10-5 minsearly5-0 minsearly0-5 minslate5-10 minslate10-15 minslate15-20minslateFrequency 33 66 22 17 10 2a) Make a cumulative frequency table for this data.b) From the table, draw a cumulative frequency diagram. Use a scale of 2cm to represent 5minutes on the horizontal axis and 1cm to represent 10 trains on the vertical axis.c) The train company guarantees that its services will not be more than 7 minutes late. Useyour graph to check what percentage were outside the guarantee.4. A large electrical retailer keeps stocks of television sets in its main warehouse for deliveryto its shops. Over a period of 1 year (365 days) the number of TV’s in the warehouse aregiven in the table below.No. of TV’s in warehouse 50-100 101-150 151-200 201-250 251-300 301-350No of days (frequency) 5 27 77 145 83 28a) Make a cumulative frequency table for this data.b) Draw a cumulative frequency diagram using a scale of 2cm to represent 40 TV’s on thehorizontal axis, and 2cm to represent 40 days on the vertical axis.It is the policy of the company to keep a stock of between 130 and 260 TV’s.c) For approximately how many days was the stock within these limits?d) A stock of 110 TV’s is regarded as the minimum quantity that the warehouse shouldhave. For approximately how many days was the stock below the minimum requirement?