49. Suppose that a particular light bulb is advertised as having an average lifetime of 2,000 hours and is known to satisfy an exponential failure law. Suppose for simplicity that the bulb is used continuously. Find the probability that the bulb lasts a. More than 3,000 hours. b. Less than 1,500 hours. c. Between 2,000 and 2,500 hours.

A life insurance salesman operates on the premise that the probability that a man reaching his sixtieth birthday will not live to his sixty-first birthday is 0.05. On visiting a holiday resort for seniors, he sells 8 policies to men approaching their sixtieth birthdays. Each policy comes into effect on the birthday of the insured and pays a fixed sum on death. All 8 policies can be assumed to be mutually independent. Provide answers to the following to 3 decimal places. Part a) What is the expected number of policies that will pay out before the insured parties have reached age 61? Part b) What is the variance of the number of policies that will pay out before the insured parties have reached age 61? Part c) What is the probability that at least two policies will pay out before the insured parties have reached age 61?

6) The following figure shows that the probability of a plant flowering in 1987 was related to its initial size (as defined by leaf area) in 1984. Also, for a given-size plant, the probability of flowering declines as a function of previous allocation to reproduction (measured as the number of fruits produced during 1984-1986). Based on this figure, approximately how large (leaf area in cm3) would a plant that has produced three fruits over the last three years have to be in order to have an approximately 50% (0.50) probability of flowering? Probability of flowering in 1987 1.0 0.8 0.6 0.4 0.2 00000 ***** AM 100 Question 6 options: 100 cm3 150 cm3 300 cm3 250 cm3 00 .. 200 300 Leaf area in 1984 (cm²) O fruits 1 fruit ▲ 2 fruits 3 fruits 400 500

11. fast please The life (years), of a battery is approximately exponentially distributed with decay parameter of 0.2. Suppose this type of battery has a warranty period of 4 years. What is the probability that the battery will need to be replaced within the warranty period? Group of answer choices 0.5507 0.2621 0.8413 0.4493

In this example, what is the probability of a person who lives in a single home with a single family with multiple generations getting infected with Covid? Enter the answer to three digits after the decimal place. 

The time (in years) after reaching age 60 that it takes an individual to retire is approximately exponentially distributed with a mean of about 6 years. Suppose we randomly pick one retired individual. We are interested in the time after age 60 to retirement. Find the probability that the person retired after age 70. (Round your answer to four decimal places.) In a room of 1,000 people over age 82, how many do you expect will NOT have retired yet? (Round your answer to the nearest whole number.) ch5#4

2. You are to wait for the first car to arrive at an inspection station. It is believed that the waittime (in minutes) follows an Exponential distribution with parameter ✓ = 10 minutes. a. You are to wait for 10 independent cars to arrive (cars arrive one by one to the station, thinkof X i as the time for the i-th car). How long do you expect to wait to complete this task? Howmuch do you expect the true wait time to vary around the expected time?

Show work for every step. Two types of customers (Preferred and Regular) call a service center. Preferred customers call with rate 3 per hour, and Regular customers call with rate 5 per hour. The interarrival times of the calls for each customer type are exponentially distributed. If the call center opens at 8:00 AM, what is the probability that the first call (regardless of customers type who calls) is received before 8:15 AM?

An engineer designs a circuit, seen below. In this system, if the first component fails, the functionality moves immediately to the second component and so on. The system only fails when the fifth component fails. Each component has a lifetime that is exponentially distributed with λ = 0.01 and components fail independently of one another. Define A, to be the length of time component i lasts. Let Y = the time at which the new system fails. Given 2 لنا 5 A-Exponential (0.01) Y=A1+A2+A3+A4+A5 1. Find the probability that this new system will last fewer than 50 hours.