A supermarket selected a sample of 240 of its customers and measured how long th

Question

A supermarket selected a sample of 240 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 86% of its customers to be checked out in 8.6 minutes or less. From the data, the 90th and 60th percentiles were computed to be 8.6 minutes and 7.3 minutes, respectively. The range of the data was 14 minutes and the fastest anyone was checked out was 1.9 minutes. Step 4 of 5: Based on the given information, determine if the following statement is true or false. Ninety percent of the customers will be checked out in 5 minutes or less.

part 2

A supermarket selected a sample of 240 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 86% of its customers to be checked out in 8.6 minutes or less. From the data, the 90th and 60th percentiles were computed to be 8.6 minutes and 7.3 minutes, respectively. The range of the data was 14 minutes and the fastest anyone was checked out was 1.9 minutes. Step 5 of 5: What percentage of the customers were checked out between 7.3 and 8.6 minutes?

Explanation / Answer

Step 4 of 5:

90th percentile - The value that is greater than 90% of the overall data set. ---> 8.6 minutes

This means 90% of the people had to wait for less than or equal to 8.6 minutes.

and 60% of the people had to wait for less than 7.3 minutes.

Statement: Ninety percent of the customers will be checked out in 5 minutes or less.

The people between 60% and 90% of the population had a waiting time in the range of 7.3 mins to 8.6 mins.

So since there are DEFINITELY some people who had a waiting time between 7.3 mins to 8.6 mins, this means that 90% of the customers cannot be checked out in 5 minutes or less.

The statement is FALSE.

Step 5 of 5:

Customers checked out between 7.3 mins and 8.6 mins ---->

90th percentile - 60th percentile = the values between 90th Percentile and 60th Percentile

If there were 240 customers, then 90% x 240 = 216 customers and 60% x 240 = 144 customers.

90th percentile - 60th percentile = the values between 90th Percentile and 60th Percentile = 216 - 144 = 72

72 = 30% of 240

Therefore, Answer: 30%

Cheers!

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