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 | 5710 |\n| right shaped - small | 4546 |\n| flaked | 1218 |\n| wrong axis | 1155 |\n| chamfer wrong | 1115 |\n| crazing, cracks | 1766 |\n| wrong shape | 1365 |\n| wrong pd | 1518 |\n| spots and bubbles | 1238 |\n| wrong height | 1460 |\n| right shape - big | 1392 |\n| lost in lab | 989 |\n| spots/bubbles - intern | 973 |\n\na) find the probability that a randomly selected defect from the table will be in the categor \lost in lab\ or the category \right shape - big\.\n\ngive your answer as a fraction.\n\ngive your answer rounded to three decimal places.\n\nb) find the probability that a randomly selected defect is not in the category \lost in lab\.\n\ngiven your answer as a fraction.\n\ngive your answer rounded to three decimal places.\n\nquestion help: video 1 video 2 message instructor

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 | 5710 |\n| right shaped - small | 4546 |\n| flaked | 1218 |\n| wrong axis | 1155 |\n| chamfer wrong | 1115 |\n| crazing, cracks | 1766 |\n| wrong shape | 1365 |\n| wrong pd | 1518 |\n| spots and bubbles | 1238 |\n| wrong height | 1460 |\n| right shape - big | 1392 |\n| lost in lab | 989 |\n| spots/bubbles - intern | 973 |\n\na) find the probability that a randomly selected defect from the table will be in the categor \lost in lab\ or the category \right shape - big\.\n\ngive your answer as a fraction.\n\ngive your answer rounded to three decimal places.\n\nb) find the probability that a randomly selected defect is not in the category \lost in lab\.\n\ngiven your answer as a fraction.\n\ngive your answer rounded to three decimal places.\n\nquestion help: video 1 video 2 message instructor

Answer

Explanation:

Step1: Calculate total number of defects

Sum all frequencies: $5710 + 4546+1218 + 1155+1115+1766+1365+1518+1238+1460+1392+989+973=23345$

Step2: Calculate number of defects in "Lost in lab" or "Right shape - big"

Add frequencies of "Lost in lab" and "Right shape - big": $989 + 1392=2381$

Step3: Calculate probability for part a (fraction)

Probability $P=\frac{2381}{23345}$

Step4: Calculate probability for part a (rounded decimal)

$P=\frac{2381}{23345}\approx0.102$

Step5: Calculate probability for part b (fraction)

Probability of not "Lost in lab" is $1 - \frac{989}{23345}=\frac{23345 - 989}{23345}=\frac{22356}{23345}$

Step6: Calculate probability for part b (rounded decimal)

$P=\frac{22356}{23345}\approx0.958$

Answer:

a) $\frac{2381}{23345}$, $0.102$ b) $\frac{22356}{23345}$, $0.958$