A small company produces cylindrical wooden pegs for making garden chairs. The lengths and diameters of the 242 pegs produced yesterday have been measured independently by two employees, and their results are given in the following table.

a. On the same axes, draw two cumulative frequency graphs: one for lengths and one for diameters.

b. Correct to the nearest millimetre, the lengths and diameters of n of these pegs are equal. Find the least and greatest possible value of n.

c. A peg is acceptable for use when it satisfies both l ≥ 2.8 and d < 2.2. Explain why you cannot obtain from your graphs an accurate estimate of the number of these 242 pegs that are acceptable. Suggest what the company could do differently so that an accurate estimate of the proportion of acceptable pegs could be obtained.

Transcribed Image Text:

Length (I em) I<1.0 I< 2.0 1< 2.5 1<3.0 I<3.5 I< 4.0 I< 4.5 No. pegs (ef 8. 40 110 216 242 Camoridge Diateter (d cm) d <1.0 d<1.5 d< 2.5 d<2.0 d < 3.0 No. pegs (ef) 60 182 222 242