Question

find the indicated probabilities using the geometric distribution, the poisson distribution, or the binomial distribution. then determine if the events are unusual. if convenient, use the appropriate probability table or technology to find the probabilities. a glass manufacturer finds that 1 in every 1000 glass items produced is warped. find the probability that (a) the first warped glass item is the 11th item produced, (b) the first warped item is the first, second, or third item produced, and (c) none of the first 10 glass items produced are defective. (a) p(the first warped glass item is the 11th item produced) = 0.001 (round to three decimal places as needed.) (b) p(the first warped item is the first, second, or third item produced) = 0.003 (round to three decimal places as needed.) (c) p(none of the first 10 glass items produced are defective) = 0.990 (round to three decimal places as needed.) which of the events are unusual? select all that apply a. the event in part (a) is unusual. b. the event in part (b) is unusual. c. the event in part (c) is unusual. d. none of the events are unusual.

Explanation:

Step1: Recall the rule for unusual events

An event is unusual if its probability is less than or equal to 0.05 (a common threshold, though sometimes 0.01 is used, but here we'll check against 0.05).

Step2: Analyze part (a)

Probability \( P(\text{first warped at 11th}) = 0.001 \). Since \( 0.001 \leq 0.05 \), this event is unusual.

Step3: Analyze part (b)

Probability \( P(\text{first warped at 1st, 2nd, or 3rd}) = 0.003 \). Since \( 0.003 \leq 0.05 \), this event is unusual.

Step4: Analyze part (c)

Probability \( P(\text{none of first 10 defective}) = 0.990 \). Since \( 0.990 > 0.05 \), this event is not unusual.

Step5: Determine unusual events

From the analysis, events in (a) and (b) are unusual, so options A and B apply.

Answer:

A. The event in part (a) is unusual.
B. The event in part (b) is unusual.