Question 7
“Aqua Aqua (AA)” is a manufacturer of water purifiers. AA wants to understand the life of its RO filters. The life of a filter is measured in terms of “Litres of Water Purified (LWP)” before a warning light is raised for maintenance. A sample of 20 water purifiers were tested and the time (LWP) after which the warning light is raised for maintenance of the RO Filter was noted (data provided in Table-2). With this data, AA wants to understand the possible distribution for the life of the RO filter. To this end, it is proposed to bin the data in 4 groups “Low Life (LWP <=25)”, “Medium Life (25<LWP<=40)”, “High Life (40<LWP<=80)”, “Excellent Life (LWP>80)”.
The following Ф values are given to you, where Ф(z) indicates the area under the curve (between “0” to “LWP”) for a normal distribution with a mean of 60 and standard deviation of 24. Ф(-1.45) = 0.07; Ф(-0.83) = 0.20; Ф(+0.83) = 0.79; Ф(+1.45) = 0.93
| Sample-ID | RO Filter Life (in LWP) | Sample-ID | RO Filter Life (in LWP) |
|---|---|---|---|
| S-1 | 73 | S-11 | 70 |
| S-2 | 49 | S-12 | 47 |
| S-3 | 12 | S-13 | 78 |
| S-4 | 72 | S-14 | 15 |
| S-5 | 97 | S-15 | 54 |
| S-6 | 95 | S-16 | 61 |
| S-7 | 79 | S-17 | 91 |
| S-8 | 42 | S-18 | 61 |
| S-9 | 70 | S-19 | 26 |
| S-10 | 53 | S-20 | 64 |
Table-2
Given this information, answer the subquestions
If the life of the RO filter is expected to follow a normal distribution with a mean of 60 and standard deviation of 24, then what is the expected frequency in the “Excellent Life” bin? (Note-1: The bins DO NOT SPILT the sample space into equal areas) (Note-2: If your answer is in decimal, enter it rounded to two decimal places. For example, if your answer is “10.256”, enter it as “10.26”)