4. The life T (hours) of the lightbulb in an overhead projector follows an Exp(10)-distribution. During a normal week it is used a Po(12)- distributed number of lectures lasting exactly one hour each. Find the probability that a projector with a newly installed lightbulb functions throughout a normal week (without replacing the lightbulb).

Question 2, section 6.1

Today, the waves are crashing onto the beach every 5.1 seconds. The times from when a person arrives at the shoreline until a crashing wave is observed follows a Uniform distribution from 0 to 5.1 seconds. Round to 4 decimal places where possible. The probability that a person will be born between weeks 18 and 52 is P(18<x<52)P(18<x<52) =  The probability that a person will be born after week 40 is P(x > 40) =  P(x > 10 | x < 47) =

A recent survey of 1040 U.S. adults selected at random showed that 634 consider the occupation of firefighter to have very great prestige. Estimate the probability (to the nearest hundredth) that a U.S. adult selected at random thinks the occupation of firefighter has very great prestige.Step 1Recall that the probability of an event based on relative frequency uses the formulaprobability of event = relative frequency = fn,where f is the frequency of the event occurrence in a sample of n observations. A total of 1040 people were surveyed and 634 considered the occupation of firefighter to have very great prestige. Therefore, the sample size is n =  . The event of interest is that a U.S. adult selected at random thinks the occupation of firefighter has very great prestige. Therefore, the frequency f is equal to the number of adults who  the occupation of firefighter has very great prestige, so f =  (0.6096 answer is incorrect.) .

The time between failures of our video streaming service follows an exponential distribution with a mean of 40 days. Our servers have been running for 17 days, What is the probability that they will run for at least 97 days? (clarification: run for at least another 80 days given that they have been running 17 days). Report your answer to 3 decimal places.

Let x be a random variable that represents red blood cell count (RBC) in millions of cells per cubic millimeter of whole blood. Then x has a distribution that is approximately normal. For the population of healthy female adults, suppose the mean of the x distribution is about 4.64. Suppose that a female patient has taken six laboratory blood tests over the past several months and that the RBC count data sent to the patient's doctor are as follows. 4.9 4.2 4.5 4.1 4.4 4.3 (1) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.) x=| S= (ii) Do the given data indicate that the population mean RBC count for this patient is lower than 4.64? Use a = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. Ο Hg: μ= 4.64; H1: μ 4.64 Ο Ηρ: μ> 4.64; H1: μ = 4.64 Ho: u = 4.64; H1: u * 4.64 (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O…

The Weibull distribution is widely used in statistical problems relating to aging of solid insulating materials subjected to aging and stress. Use this distribution as a model for time (in hours) to failure of solid insulating specimens subjected to AC voltage. The values of the parameters depend on the voltage and temperature; suppose a = 2.6 and B = 220. (a) What is the probability that a specimen's lifetime is at most 250? Less than 250? More than 300? (Round your answers to five decimal places.) at most 250 less than 250 more than 300 0.7520 0.7520 0.1065 x X X (b) What is the probability that a specimen's lifetime is between 100 and 250? (Round your answer to four decimal places.) 0.6312 (c) What value (in hr) is such that exactly 50% of all specimens have lifetimes exceeding that value? (Round your answer to three decimal places.) 191 Xhr

Dandelions are studied for their effects on crop production and lawn growth. In one region, the mean number of dandelions per square meter was found to be 11.Find the probability of no dandelions in an area of 1 m².P(X=0)=P(X=0)=Find the probability of at least one dandelion in an area of 1 m².P(at least one) =Find the probability of at most two dandelions in an area of 1 m².P(X≤2)=