eyeglassomatic manufactures eyeglasses for different retailers. they test to see how many defective lenses…

eyeglassomatic manufactures eyeglasses for different retailers. they test to see how many defective lenses they made in a time period. the following table gives the type of defect and the number of lenses with that defect. assume categories are mutually exclusive.\n\n| defect type | frequency |\n|--|--|\n| scratch | 5779 |\n| right shaped - small | 4692 |\n| flaked | 1735 |\n| wrong axis | 1746 |\n| chamfer wrong | 1425 |\n| crazing, cracks | 1368 |\n| wrong shape | 1494 |\n| wrong pd | 1486 |\n| spots and bubbles | 1159 |\n| wrong height | 1897 |\n| right shape - big | 1870 |\n| lost in lab | 974 |\n| spots/bubbles - intern | 972 |\n\na) find the probability that a randomly selected defect from the table will be in the category \scratch\ or the category \wrong shape\.\ngive your answer as a fraction.\ngive your answer rounded to three decimal places.\nb) find the probability that a randomly selected defect is not in the category \scratch\.\ngiven your answer as a fraction.\ngive your answer rounded to three decimal places.\nquestion help: video 1 video 2 message instructor\nsubmit question

eyeglassomatic manufactures eyeglasses for different retailers. they test to see how many defective lenses they made in a time period. the following table gives the type of defect and the number of lenses with that defect. assume categories are mutually exclusive.\n\n| defect type | frequency |\n|--|--|\n| scratch | 5779 |\n| right shaped - small | 4692 |\n| flaked | 1735 |\n| wrong axis | 1746 |\n| chamfer wrong | 1425 |\n| crazing, cracks | 1368 |\n| wrong shape | 1494 |\n| wrong pd | 1486 |\n| spots and bubbles | 1159 |\n| wrong height | 1897 |\n| right shape - big | 1870 |\n| lost in lab | 974 |\n| spots/bubbles - intern | 972 |\n\na) find the probability that a randomly selected defect from the table will be in the category \scratch\ or the category \wrong shape\.\ngive your answer as a fraction.\ngive your answer rounded to three decimal places.\nb) find the probability that a randomly selected defect is not in the category \scratch\.\ngiven your answer as a fraction.\ngive your answer rounded to three decimal places.\nquestion help: video 1 video 2 message instructor\nsubmit question

Answer

Explanation:

Step1: Calculate total number of defects

Sum all frequencies: $5779 + 4692+1735 + 1746+1425+1368+1494+1486+1159+1897+1870+974+972$ $= 26827$

Step2: Calculate number of 'Scratch' or 'Wrong shape' defects

Number of 'Scratch' defects is $5779$, number of 'Wrong shape' defects is $1494$. So total is $5779 + 1494=7273$.

Step3: Calculate probability for part a (fraction)

Probability $P=\frac{7273}{26827}$

Step4: Calculate probability for part a (rounded)

$P=\frac{7273}{26827}\approx 0.271$

Step5: Calculate number of non - 'Scratch' defects

Total defects minus 'Scratch' defects: $26827-5779 = 21048$

Step6: Calculate probability for part b (fraction)

Probability $P=\frac{21048}{26827}$

Step7: Calculate probability for part b (rounded)

$P=\frac{21048}{26827}\approx 0.785$

Answer:

a) $\frac{7273}{26827}$, $0.271$ b) $\frac{21048}{26827}$, $0.785$