A Christmas tree light has an expected life of 210 hr and a standard deviation of 2 hr. (a) Find a bound on the probability that one of these Christmas tree lights will require replacement between 200 hr and 220 hr. (Enter your answer to two decimal places.)(b) Suppose a large city uses 160,000 of these Christmas tree lights as part of its Christmas decorations. Estimate the number of lights that are likely to require replacement between 190 hr and 230 hr of use.

A Christmas tree light has an expected life of 210 hr and a standard deviation of 2 hr. (a) Find a bound on the probability that one of these Christmas tree lights will require replacement between 200 hr and 220 hr. (Enter your answer to two decimal places.)(b) Suppose a large city uses 160,000 of these Christmas tree lights as part of its Christmas decorations. Estimate the number of lights that are likely to require replacement between 190 hr and 230 hr of use.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

Consider a cohort of patients receiving an experimental two-year treatment for a serious disease. Suppose that only 20% of the patients survive to the end of the second year. Assume CFM (constant force of mortality) within each year of treatment. Find the probability that a patient who survives the first four months dies by the end of the 20th month. Round to 4 decimal places.
Suppose that the TSH (Thyroid Stimulating Hormone) levels among healthy individuals are normally distributed with a mean of 3.3 unitsmL. Suppose also that exactly 95% of healthy individuals have TSH levels below 6.2 unitsmL. Find the standard deviation of the distribution of TSH levels of healthy individuals. Carry your intermediate computations to at least four decimal places. Round your answer to at least two decimal places.
Reliability testing of the new 2.0 liter Chevy automotive engine has resulted in a time to failure distribution which is lognormal with = 90,000 mi. and s = 0.60. Find: med %3D a. R(40,000 mi.) b. MTTF and Std. Dev. c. R(90,000|40,000) d. t .90
If the power received at the MU is lognormal with standard deviation of 9dB, the outage probability can be expressed as erfc(x)/2. determine the value of x given the average power received is -97dBm and the threshold power is -101dBm.
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.
The type of battery in Jim's laptop has a lifetime (in years) which follows a Weibull distribution with parameters a = 2 and B = 4. The type of battery in Jim's tablet has a lifetime (in years) which follows an exponential distribution with parameter A = 1/4. Find the probability that the lifetime of his laptop battery is less than 2.5 years and that the lifetime of his tablet battery is less than 3.2 years. (Answer as a decimal number, and round to 3 decimal places).
Assume that adults have IQ scores that are normally distributed with a mean of μ=105 and a standard deviation σ=15. Find the probability that a randomly selected adult has an IQ less than 123.
The lifespans of light bulbs are known to follow an exponential distribution. The exponential distribution, often denoted exp(β), is characterized by a single mean parameter β. The exponential distribution has a unique property that its standard deviation is equal to its mean. Suppose you order 100 light bulbs known to each have lifespans (in years) distributed according to exp(4). What is the probability that the average lifespan of your 100 light bulbs exceeds 5 years? (Using R it possible)
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 mean of this distribution is The standard deviation is The probability that wave will crash onto the beach exactly 1.4 seconds after the person arrives is P(x = 1.4) = The probability that the wave will crash onto the beach between 1.3 and 4.7 seconds after the person arrives is P(1.3 < x < 4.7) = The probability that it will take longer than 3.92 seconds for the wave to crash onto the beach after the person arrives is P(x > 3.92) = Suppose that the person has already been standing at the shoreline for 1.1 seconds without a wave crashing in. Find the probability that it will take between 2.4 and 3.8 seconds for the wave to crash onto the shoreline. 84% of the time a person will wait at least how long before the wave crashes in?…
please answer this question within 30 minutes. i will upvote.
If the iron cutting machine in a factory works continuously for a certain period of time under the same conditions, it goes into malfunction. In this type of failure, the machine takes 24 hours to cool down. After the machine has cooled down, it continues to work the next day. Assume that the running time (minutes) of this machine until it malfunctions has a normal distribution. The working time of the iron cutting machine until the failure was measured for 9 different days, which were chosen at random. Continuous working time (minutes): 14-26-18-29-12-19-22-30-19 a) Establish the 95% confidence interval for the average uninterrupted working time of this iron cutting machine and interpret the result.b) The factory chief claims that the average continuous operating time of the machine is less than 23 minutes. Test the claim that the average continuous working time of this iron cutting machine is less than 23 minutes at the 0.05 significance level and the result isPlease comment.