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.

defect type	frequency
right shaped - small	4525
flaked	1169
wrong axis	1725
chamfer wrong	1417
crazing, cracks	1687
wrong shape	1135
wrong pd	1742
spots and bubbles	1733
wrong height	1344
right shape - big	1237
lost in lab	981
spots/bubbles - intern	977

a) find the probability that a randomly selected defect from the table will be in the categor \wrong height\ or the category \spots/bubbles - intern\.
give your answer as a fraction.
give your answer rounded to three decimal places.
b) find the probability that a randomly selected defect is not in the category \wrong height\.
given your answer as a fraction.
give your answer rounded to three decimal places.

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