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 | 5621 |\n| right shaped - small | 4525 |\n| flaked | 1169 |\n| wrong axis | 1725 |\n| chamfer wrong | 1417 |\n| crazing, cracks | 1687 |\n| wrong shape | 1135 |\n| wrong pd | 1742 |\n| spots and bubbles | 1733 |\n| wrong height | 1344 |\n| right shape - big | 1237 |\n| lost in lab | 981 |\n| spots/bubbles - intern | 977 |\n\na) find the probability that a randomly selected defect from the table will be in the categor \wrong height\ or the category \spots/bubbles - intern\.\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 \wrong height\.\ngiven your answer as a fraction.\ngive your answer rounded to three decimal places.

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 | 5621 |\n| right shaped - small | 4525 |\n| flaked | 1169 |\n| wrong axis | 1725 |\n| chamfer wrong | 1417 |\n| crazing, cracks | 1687 |\n| wrong shape | 1135 |\n| wrong pd | 1742 |\n| spots and bubbles | 1733 |\n| wrong height | 1344 |\n| right shape - big | 1237 |\n| lost in lab | 981 |\n| spots/bubbles - intern | 977 |\n\na) find the probability that a randomly selected defect from the table will be in the categor \wrong height\ or the category \spots/bubbles - intern\.\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 \wrong height\.\ngiven your answer as a fraction.\ngive your answer rounded to three decimal places.

Answer

Explanation:

Step1: Calculate total number of defects

Sum all frequencies. $5621 + 4525+1169 + 1725+1417+1687+1135+1742+1733+1344+1237+981+977=24199$

Step2: Calculate probability for part a

The frequency of "Wrong height" is 1344 and of "Spots/bubbles - intern" is 977. The number of favorable outcomes for part a is $1344 + 977=2321$. The probability $P(a)$ as a fraction is $\frac{2321}{24199}$. Rounding to three - decimal places, $P(a)=\frac{2321}{24199}\approx0.096$.

Step3: Calculate probability for part b

The probability that a defect is in the "Wrong height" category is $P(\text{Wrong height})=\frac{1344}{24199}$. The probability that a defect is not in the "Wrong height" category is $P(b)=1 - \frac{1344}{24199}=\frac{24199 - 1344}{24199}=\frac{22855}{24199}$. Rounding to three - decimal places, $P(b)=\frac{22855}{24199}\approx0.944$.

Answer:

a) $\frac{2321}{24199}$, 0.096 b) $\frac{22855}{24199}$, 0.944