# Calculate an estimate for the mean of the waiting times,by using an appropriate approximation to represent each interval.A survey is carried out to find the waiting times for 100 customers at a...

Calculate an estimate for the mean of the waiting times,by using an appropriate approximation to represent each interval.

A survey is carried out to find the waiting times for 100 customers at a supermarket. The waiting time(seconds) for 0-30, the number of customers is 5. The waiting time(WT) for 30-60, the no.of customers is 15. The WT for 60-90,the no.of customers is 33.The WT for 90-120,the no.of customers is 21.The WT for 120-150,the no.of customers is 11.The WT for 150-180,the no.of customer is 7.The WT for 180-210,the no.of customers is 5. The WT for 210-240,the no.of customers is 3.

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### 1 Answer

The survey was carried out to determine the waiting time for a group of 100 people. The result obtained is expressed in the following table with the time range followed by the number of people that had a waiting time lying in the range.

0 - 30 : 5

30 - 60 : 15

60 - 90 : 33

90 - 120 : 21

120 - 150 : 11

150 - 180 : 7

180 - 210 : 5

210 - 240: 3

Take the mid point of each range to calculate the weighted average waiting time.

T = (15*5 + 45*15 + 75*33 + 105*21 + 135*11 + 165*7 + 195*5 + 225*3)/100

=> 97.2

**The mean of the waiting time is approximately 97.2 seconds.**