7. A supermarket selected a sample of 180 of its customers and measured how long

Question

7. A supermarket selected a sample of 180 of its customers and measured how long they took to be served at the checkout counter. If too many customers wait too long, the supermarket intends to hire more checkout personnel. Specifically, the supermarket would like at least 89% of its customers to be checked out in 8.9 minutes or less. From the data, the 90th and 60th percentiles were computed to be 8.5 minutes and 7.2 minutes, respectively. The range of the data was 13 minutes and the fastest anyone was checked out was 1.9 minutes. Step 1: (2 points) What was the longest time (in minutes) anyone waited in line? (Round your answer to 1 decimal place) Z Step 2: 2 points The median of the data does not exceed 7.2 minutes. O True False Step 3: (2 points Approximately how many customers waited at most 7.2 minutes to be checked out? Step 4: sep 4 Ninety perc (2 points Ninety percent of the customers will be checked out in 7 minutes or less.

Explanation / Answer

Step 1 : The range = 13 minutes

so maximum waiting time = 13 + 1.9 = 14.9 minutes

Step 2 :

Here 7.2 is the 60th percentile so obviously median is not greater than 7.2 minutes

Step 3 :

Here 60% is 7. minutes so approximately 0.60 * 180 = 108 customers wait at most 7.2 mins to be checked out.

Step 4:

SO here we can say that the statement is wrong as 90% of customers will not checked out in 7 mins. it will be 8.5 minutes or less.

Step 5

Here the percentage of the customers were checked out in between 7.2 minutes and 8.5 minutes are 90% - 60% = 30%.

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