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	4546
flaked	1218
wrong axis	1155
chamfer wrong	1115
crazing, cracks	1766
wrong shape	1365
wrong pd	1518
spots and bubbles	1238
wrong height	1460
right shape - big	1392
lost in lab	989
spots/bubbles - intern	973

a) find the probability that a randomly selected defect from the table will be in the categor \lost in lab\ or the category
ight shape - big\.

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 \lost in lab\.

given your answer as a fraction.

give your answer rounded to three decimal places.

question help: video 1 video 2 message instructor

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) $\frac{22356}{23345}$, $0.958$