Answer:
a) 35%
b) 19 minutes
Step-by-step explanation:
The graph for this question is attached in the image below.
Part a) Percent of calls that lasted 30 minutes or more
As seen in the graph, the x-axis represent the duration of the call in minutes and y-axis represent the cumulative frequency of the calls.
From the graph we can see that the cumulative frequency against the point 30 minutes is about 65%. This means, 65% of the calls lasted for less than 30 minutes.
Since, out of 100%, 65% of the calls lasted for less than 30 minutes, the percentage of call that lasted for 30% or more would be:
100% - 65% = 35%
This means, 35% of calls lasted 30 minutes or more.
Part b) The interquartile range (IQR) of the distribution.
Interquartile range is defined as the difference of the 3rd Quartile and the 1st Quartile.
3rd Quartile is the point, below which 75% of the data values are present.
1st Quartile is the point, below which 25% of the data values are present.
So, from the cumulative frequency graph we have to look for the values on time axis against the cumulative frequency of 25% and 75%.
The amount of time against 25% cumulative frequency is approximately 13 minutes.
So, 1st Quartile = 13 minutes
The amount of time against 75% cumulative frequency is approximately 32 minutes.
So, 3rd Quartile = 32 minutes
Therefore,
IQR = 3rd Quartile - 1st Quartile
IQR = 32 - 13
IQR = 19 minutes
The interquartile range (IQR) of the distribution is 19 minutes.
