Question 6
The Following Comprehension and Related Subquestions are Purely Hypothetical A manufacturer produces lenses for sunglasses. In a given day, a total of 100 products were produced. Products produced usually can have scratches. The manufacturer is interested to see if the length of the scratches on produced lenses is normally distributed. Hence, based on the production of 100 lenses, he has identified the length of scratch on each lens and the grouped data is presented to you in Table-2. Further, from sample, the manufacturer has computed the standard deviation to be 1.00. Based on the production lot of 100 units (given sample), you are asked to check if the “Length of Scratches on produced lenses” follows a Normal Distribution. Given this information, answer the given subquestions.
| Length of Scratches | Number of lenses with scratches of specified length |
|---|---|
| 0.00 mm to 1.00 mm | 30 |
| 1.01 mm to 2.00 mm | 35 |
| 2.01 mm to 3.00 mm | 15 |
| 3.01 mm to 4.00 mm | 20 |
Table-2: Data on Number of products with scratches
What would be the mean of the distribution, if you want to check the hypothesis “The length of scratches on a produced lens follows a Normal Distribution”? [Note: Enter your answer rounded to two decimal places. For example, if your answer is 1.235 then enter the answer as “1.24”]