An LED light bulb has an exponentially distributed life expectancy, with a mean time of 5000 hours. What is the probability a light bulb will: a) Last more than 4000 hours? b) The bulb has already lasted 5000 hours. What is the probability it will last more than 9000 hours?

Q: The probability that a region prone to hurricanes will be hit by a hurricane in any single year is…

A: Solution: The probability that a region prone to hurricanes will be hit by a hurricane in any single…

Q: .What is the probability that a random fastball exceeds 170 km/h?

A: Let X denote the speeds of a baseball pitcher's fastballs. It is given that The distribution of X is…

Q: According to a 2019 survey by Sleepopolis, 34% of American adults sleep with some form of "comfort…

A: Solution: From the given information, p=0.34 and n=400.

Q: A recent study for Las Vegas showed that the probability of an individual resident moving in a given…

A: Solution: Let X be the number of times an individual will move and n be the number of years. From…

Q: On average, a textbook author makes 1.5 word-processing errors per page on the first draft of her…

A: Solution: Let X be number of word-procession errors per 2 pages on the first draft. Since it is a…

Q: A batch of bulbs have a mean life of 1000 hours. Only one bulb is used at a time, and after each…

A: See the handwritten solution

Q: One interpretation of a baseball player's batting average is as the empirical probability of getting…

A: Given Data: Let X represent the random variable p=0.291 n=4   X~ Binomial(4, 0.291)

Q: The life of a power transmission tower is exponentiallydistributed, with mean life 25 years. If…

A: From the given information, it can be observed that the life of a power transmission tower is…

Q: According to a survey, 70% of adults believe that every university student should take at least one…

A: a) Given information: p=70%=0.70 n=sample size=14 Let X be the number of adults hold to view follows…

Q: The die is constructed so that even numbers are twice as likely to occur as the odd number. This die…

A: Probability is simply defined as the ratio of favorable outcomes (s) to the total number of possible…

Q: Assume that there is a 10% rate of disk failure in a year  A) if all your computer data is stored…

A: P[a disk failure]=0.1,  (A) P[at least one working drive out of two]=1-P[none are working out of…

Q: The life of a power transmission tower is exponentially distributed, with mean life 25 years. If…

A:

Q: Suppose a birth control pill is 97% effective in preventing pregnancy. (Round your answers to three…

A: Given, birth control pill is 97% effective in preventing pregnancy. (a) 0.97^200 = 0.0023 = 0.002

Q: The average number of diesel tankers arriving each day at a certain port city is known to be 5. What…

A:

Q: A single die is rolled three times. What is the probability that a 1 will show on the upward face at…

A: A single die is rolled 3 times Total Sample Space = 63 = 216 Probability of not showing 1 = 56…

Q: When studying radiactive material, a nuclear engineer found that over 365 days, 1,000,000 radiactive…

A:

Q: A parking enforcement officer has a quota of 5 citations to issue by the end of the shift. Assume…

A: Number of citation to be issued at end is 5. The probability of given car has a violation is…

Q: what is the probability that it actually emits excessive amounts of emissions?

A: Define some events A : A car emits excessive amounts of emissions. B : A car does not emit excessive…

Q: Suppose a birth control pill is 98% effective in preventing pregnancy. (Round your answers to three…

A: Let us denote X= number of non-pregnant women  n= number of trials= 100 p= probability of a success=…

Q: According to the National Center for HealthStatistics, life expectancy for a 70-year-old African…

A: Mean life expectancy 1λ=12.3 So, λ=112.3  Let X~Exp112.3

Q: The time between arrivals of vehicles at a particular intersection follows an exponential…

A: From the provided information, Mean (µ) = 12 For exponential distribution, the probability formula…

Q: The annual volume of rain (in mm) in a certain region is normally distributed with μ = 40 and a σ =…

A:

Q: Assume that the mortality rate of a unicorn increases by 10% every year and assume that a proportion…

A: Given that the mortality rate of a unicorn increases by 10% every year and assume that a proportion…

Q: A die is rolled 20 times and the number of twos that come up is tallied. Find the probability of…

A: Given problem is : A die is rolled 20 times and the number of twos that come up is tallied. Find…

Q: Assume that a vending machine dispenses coffee in amounts that vary uniformly between 7.4 and 8.2…

A:

Q: Assume that the incidence of the HIV virus in a particuar population is 4% and that the test…

A: Let us denote  A= actually has the virus T=tested positive Given that P(A)=4%=0.04 P(T|A)=90%=0.90…

Q: A certain airport receives on an average of 4 aircrafts per hour. What is the probability that no…

A:

Q: Suppose that the average number of accidents occurring weekly on a par- ticular stretch of a highway…

A:

Q: (a) What is the probability that a laser fails before 5800 hours? (b) What is the life in hours that…

A:

Q: The mean number of customers arriving at a bank during a 15-minute period is 10. Find the…

A: Suppose random variable X defines the number of customers arriving at a bank during a 15-minute…

Q: an observer counts 36O vehicles per hour at a highway. estimate the probability of having more than…

A: A observer count 360 vehicle per hour at a highway.

Q: A die is rolled 20 times and the number of twos that come up is tallied. Find the probability of…

A: Given that, A die is rolled 20 times and the number of twos that come up is tallied.

Q: an observer counts 360 vehicles per hour at a highway, estimate the probability of having more than…

A: The arrival rate is 360 per hour. The mean arrival time is 36060=6 vehicles per minute Also 660=0.1…

Q: Assume that there is a 6% rate of disk drive failure in a year. If all your computer data is stored…

A: There was 6% rate of disk drive failure in a year. This means that 94% rate of disk drive does not…

Q: At a certain bank the amount of time that a customer spends being served by a teller is exponential…

A: The exponential mean of customer served by teller is 3 minutes.

Q: When studying radioactive material, a nuclear engineer found that over 365 days, 1,000,000…

A: Solution is written in below steps.

Q: A six-sided die, in which each side is equally likely to appear, is repeatedly rolled until the…

A: Let S A be the  X1+X2+X3+.......+X140 ,   where Xirepresents number obtained in the ith roll

Q: A six-sided die is rolled twelve times. What is the probability that the die will show an even…

A: Let p be the probability of getting an even number. Then p = 3/6 = 0.5 Let X denote the number of…

Q: Based on data covering two consecutive school years, the National Safety Council found that fourth…

A: It is given that injuries rate is 2.4 per 100,000 students-day. Thus, the average number of student…

Q: In a factory, there were 12 accidents involving machinery in the last six months.  (d) Calculate…

A: Given, In a factory, there were 12 accidents in the last 6 months => 12/6 = 2 accidents per month…

Q: An aircraft is excepted to land in the prescribed recovery zone with probability of 0%. In a time, 5…

A: Note:  Please repost remaining questions as i can answer only 1 question as per my policy.   1)…

Q: with a mean life of 500 hours. Suppose that the component was in operation for 400 hours. What is…

A: Since you have asked multiple question, according to our guidelines we will solve the first question…

Q: Suppose the average tread-life of a certain brand of tire is 45,000 miles and that this mileage…

A:

Q: Another engineer is testing a different set of chips from a different wafer and hasn't seen a…

A: No. of chip tests = 200.  There has no been a defective in the past 50 chips.  But here, this wont…

Q: a. What is the probability that the car battery will be dead in less than 12797 miles?

A: Let , X be the number of miles that a particular car can run before its battery wears out Here , X…

Q: A single die is rolled three times. What is the probability that a 3 will show on the upward face at…

A: We will find the probability that 3 does not show at all.  There are 6 numbers on a die. Except "3"…

Q: When rolling a die 142 times, what is the probability of rolling a 6 greater than 20 times?

A: np = 142/6 = 23.67 >10  n(1-p)  118.33 >10 ============ Normal approximation to binomial dist…