(a) What is the probability that there are no major crac 20 km stretch of the highway? (b) What is the probability that there are two major cra 20 km stretch of the highway? (c) What is the standard deviation of the distance t major cracks?

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Q.4-102 A B C D E F
(d) What is the probability of no sighting within three years?
4-101. According to results from the analysis of chocolate bars
in Chapter 3, the mean number of insect fragments was 14.4
in 225 grams. Assume that the number of fragments follows a
Poisson distribution.
(a) What is the mean number of grams of chocolate until a
fragment is detected?
(b) What is the probability that there are no fragments in a
28.35-gram chocolate bar?
(c) Suppose you consume seven 28.35-gram bars this week.
What is the probability of no insect fragments?
4-102. The distance between major cracks in a highway fol-
lows an exponential distribution with a mean of 10 km.
(a) What is the probability that there are no major cracks in a
20 km stretch of the highway?
(b) What is the probability that there are two major cracks in a
20 km stretch of the highway?
(c) What is the standard deviation of the distance between
major cracks?
(d) What is the probability that the first major crack occurs
between 24 and 30 km of the start of inspection?
Transcribed Image Text:(d) What is the probability of no sighting within three years? 4-101. According to results from the analysis of chocolate bars in Chapter 3, the mean number of insect fragments was 14.4 in 225 grams. Assume that the number of fragments follows a Poisson distribution. (a) What is the mean number of grams of chocolate until a fragment is detected? (b) What is the probability that there are no fragments in a 28.35-gram chocolate bar? (c) Suppose you consume seven 28.35-gram bars this week. What is the probability of no insect fragments? 4-102. The distance between major cracks in a highway fol- lows an exponential distribution with a mean of 10 km. (a) What is the probability that there are no major cracks in a 20 km stretch of the highway? (b) What is the probability that there are two major cracks in a 20 km stretch of the highway? (c) What is the standard deviation of the distance between major cracks? (d) What is the probability that the first major crack occurs between 24 and 30 km of the start of inspection?
10-6)(80
146
Chapter 4/Continuous Random Variables and Probability Dis
(e) What is the probability that there are no major cracks in
two separate 10 km stretches of the highway?
(f) Given that there are no cracks in the first 10 km inspected,
what is the probability that there are no major cracks in the
next 20 km inspected?imo odi noowiod on
4-103. The lifetime of a mechanical assembly in a vibration
test is exponentially distributed with a mean of 400 hours.
(a) What is the probability that an assembly on test fails in less
than 200 hours?
(b) What is the probability that an assembly operates for more
than 500 hours before failure?
Indi ilidsdong
(c) If an assembly has been on test for 400 hours without a fail-
ure, what is the probability of a failure in the next 100 hours?
(d) If 10 assemblies are tested, what is the probability that
noi at least one fails in less than 100 hours? Assume that the
assemblies fail independently.
(e) If 10 assemblies are tested, what is the probability that all
have failed by 800 hours? Assume that the assemblies fail
independently.
4-104. The time between arrivals of small aircraft at a county
airport is exponentially distributed with a mean of one hour.
(a) What is the probability that more than two aircraft arrive
aib vllsuns
within an hour?
(b) If 30 separate one-hour intervals are chosen, what is the
probability that no interyal containe
Transcribed Image Text:10-6)(80 146 Chapter 4/Continuous Random Variables and Probability Dis (e) What is the probability that there are no major cracks in two separate 10 km stretches of the highway? (f) Given that there are no cracks in the first 10 km inspected, what is the probability that there are no major cracks in the next 20 km inspected?imo odi noowiod on 4-103. The lifetime of a mechanical assembly in a vibration test is exponentially distributed with a mean of 400 hours. (a) What is the probability that an assembly on test fails in less than 200 hours? (b) What is the probability that an assembly operates for more than 500 hours before failure? Indi ilidsdong (c) If an assembly has been on test for 400 hours without a fail- ure, what is the probability of a failure in the next 100 hours? (d) If 10 assemblies are tested, what is the probability that noi at least one fails in less than 100 hours? Assume that the assemblies fail independently. (e) If 10 assemblies are tested, what is the probability that all have failed by 800 hours? Assume that the assemblies fail independently. 4-104. The time between arrivals of small aircraft at a county airport is exponentially distributed with a mean of one hour. (a) What is the probability that more than two aircraft arrive aib vllsuns within an hour? (b) If 30 separate one-hour intervals are chosen, what is the probability that no interyal containe
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