Pt2520 Unit 1 Practice Midterm
STAT220
Spring 2012
Practice Midterm
1. Let A and B be events such that P(A) = 0.25 and P(B) = 0.16. Find P(A|B) if
(a) P(A B) = 0.06
(b) P(B|A) = 0.4
(c) P(AB) = 0.33
(d) A and B are independent
(e) A and B are mutually exclusive
2. Among employees of a certain firm, 70% know C/C++, 60% know Java, and 90% know at least one of the two languages. (a) What is the probability that a selected programmer knows both languages?
(b) What is the probability that a selected programmer knows C/C++ but not Java?
(c) What is the probability that a selected programmer knows only one of the two languages?
(d) If a programmer knows Java, what is the probability that he/she knows C/C++?
(e) If a programmer knows C/C++, what is the probability that he/she …show more content…
Suppose the lifetime of a certain type of component is a random variable having an exponential distribution with mean lifetime 5 years.
(a) What is the probability that a selected component of this type will last more than 4 years?
(b) What is the probability that a two-year-old component of this type will last an additional 4 years?
(c) What is the 25th percentile of the lifetimes of such components?
(d) What is the probability that the mean lifetime of 64 randomly selected components is less than 4.8 years?
16. In the Ames Bank (open 24h every day) 5 customers arrive on average during an hour. For the following questions state each time which random variable you use and what distribution assumption you make.
(a) What is the probability that during an hour no customer arrives?
(b) What is the probability that during an hour more than 7 customers arrive?
(c) What is the probability that there’s more than 30 minutes between the 2nd and 3rd customer on New
Year’s Day?
(d) Starting at some time 0. What is the probability that the first customer arrives after exactly 10 min?
Within the first ten minutes?
(e) How many minutes do you expect to wait on average between arrivals?
(f) How many customers do you expect to arrive within 3 hours?
Spring 2012
Practice Midterm
1. Let A and B be events such that P(A) = 0.25 and P(B) = 0.16. Find P(A|B) if
(a) P(A B) = 0.06
(b) P(B|A) = 0.4
(c) P(AB) = 0.33
(d) A and B are independent
(e) A and B are mutually exclusive
2. Among employees of a certain firm, 70% know C/C++, 60% know Java, and 90% know at least one of the two languages. (a) What is the probability that a selected programmer knows both languages?
(b) What is the probability that a selected programmer knows C/C++ but not Java?
(c) What is the probability that a selected programmer knows only one of the two languages?
(d) If a programmer knows Java, what is the probability that he/she knows C/C++?
(e) If a programmer knows C/C++, what is the probability that he/she …show more content…
Suppose the lifetime of a certain type of component is a random variable having an exponential distribution with mean lifetime 5 years.
(a) What is the probability that a selected component of this type will last more than 4 years?
(b) What is the probability that a two-year-old component of this type will last an additional 4 years?
(c) What is the 25th percentile of the lifetimes of such components?
(d) What is the probability that the mean lifetime of 64 randomly selected components is less than 4.8 years?
16. In the Ames Bank (open 24h every day) 5 customers arrive on average during an hour. For the following questions state each time which random variable you use and what distribution assumption you make.
(a) What is the probability that during an hour no customer arrives?
(b) What is the probability that during an hour more than 7 customers arrive?
(c) What is the probability that there’s more than 30 minutes between the 2nd and 3rd customer on New
Year’s Day?
(d) Starting at some time 0. What is the probability that the first customer arrives after exactly 10 min?
Within the first ten minutes?
(e) How many minutes do you expect to wait on average between arrivals?
(f) How many customers do you expect to arrive within 3 hours?