# 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.

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.

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