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A store receives customer satisfaction ratings on a scale of 1-50 (both inclusive). In the first five ratings the store received an average rating of 27. What is the least value the Store can receive on the 6th rating and still be able to have an average of at least 35 in the first 10 ratings?

Solution:

Since, the first five ratings received an average rating of 27.

Therefore, sum of the first 5 ratings = 5 * 27 (as Average = Sum of observation / Number of observations)  = 135.

In order for average to be at least 35 for the first 10 ratings, the sum of the ratings should be at least 35 * 10 = 350

Hence the sum of observations (6th to 10th) must be at least 350 – 135 = 215.

Also, our objective is to find the least value for 6th customer rating.

Therefore, we need to maximize 7th, 8th, 9th and 10th rating.

The maximum value of any rating can be 50. (given in the question)

Therefore, least value of 6th rating will be as follows

6th rating + 4(50) = 215

Hence 6th rating minimum value will be 15.