Suppose that the time to failure (in hours) of fans in a personal computer can be modeled by anexponential distribution with 1 = 0.0003.What proportion of the fans will last at most 10,000 hours?What proportion of the fans will last at least 7000 hours?a. 0.0498, 0.1225O b.0.9502, 0.1225O c. 0.0498, 0.8775O d. NONE

Answered: Image /qna-images/answer/bcc3e320-7c07-4c6e-9f84-7c7dbcd1ae14.jpg

Answered: Suppose that the time to failure (in…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The time (in years) after reaching age 60 that it takes an individual to retire is approximately exponentially distributed with a mean of about 7 years. Suppose we randomly pick one retired individual. We are interested in the time after age 60 to retirement. In a room of 1,000 people over age 81, how many do you expect will NOT have retired yet? (Round your answer to the nearest whole number.)
Suppose that the length of long distance phone calls, mea- sured in minutes, is known to have an exponential distribution with the average length of a call equal to 15 minutes. Find the CDF.
48. The lifetime of certain electronic components is assumed to have an exponential distribution. Assuming the average lifespan of these components is 250 hours, ... (a) Find the pdf of the lifespan of these components. (b) Find the median lifespan of these components. (c) Find the proportion of components with a lifespan less than 200 hours. (d) Find the proportion of components with a lifespan greater than 275 hours.
During a professor's office hours, students arrive, on average, every ten minutes. Assume that the distribution of the time between arrivals follows an exponential distribution. Suppose that a student has just left. Suppose that a student has just left. Only 25% of the time will the professor have to wait approximately how long or longer before the next student shows up?
An article in a magazine discussed the length of time till failure of a particular product. At the end of the product's lifetime, the time till failure is modeled using an exponential distribution with a mean of 500 thousand hours. In reliability jargon this is known as the "wear-out" distribution for the product. During its normal (useful) life, assume the product's time till failure is uniformly distributed over the range 200 thousand to 1 million hours. Complete parts a through c. a. At the end of the product's lifetime, find the probability that the product fails before 600 thousand hours. (Round to four decimal places as needed.)
In a certain year, the percent of persons (ages five and older) in each state who speak a language at home other than English was approximately exponentially distributed with a mean of 9.352. Suppose we randomly pick a state. Find the probability that the percent is between 6 and 17. (Round your answer to four decimal places.)
A light fixture contains five lightbulbs. The lifetime of each bulb is exponentially distributed with mean 199.0 hours. Whenever a bulb burns out, it is replaced. Let T be the time of the first bulb replacement. Let X1, i = 1, . . . , 5, be the lifetimes of the five bulbs. Assume the lifetimes of the bulbs are independent. 1. Find P( X1 > 100). (Round the final answer to four decimal places.) 2. Find P( X1 > 100 and X2 > 100 and • • • and X5 > 100). (Round the final answer to four decimal places.) 3. Find P(T ≤ 100). (Round the final answer to four decimal places.) 4. Let t be any positive number. Find P(T ≤ t), which is the cumulative distribution function of T. 5. Find the mean of T. (Round the final answer to two decimal places.)
Previously, De Anza's statistics students estimated that the amount of change daytime statistics students carry is exponentially distributed with a mean of $0.88. Suppose that we randomly pick 25 daytime statistics students. Find the probability that an individual had between $0.80 and $1.00. Graph the situation, and shade in the area to be determined.
The Transylvania hypothesis claims that the full moon has an effect on health-related behavior. A study investigating this effect found a significant relationship between the phase of the moon and the (x-4) + 100 where y is the number of consultations as a percentage of the daily mean and x is the days since the last full 15.12 number of general practice consultations nationwide, given by y = 1.9 cos moon. a. What is the period of this function? What is the significance of this period? The period is days. (Round to two decimal places as needed.) Choose the correct meaning of the period p in the context of the problem. The x-distance between the maximum and the minimum of the graph is p. Every p days there is a full moon. There were p% more consultations when there was a full moon. The average number of daily consultations is p. b. If there was a full moon on April 7, on what day in April does this formula predict the maximum number of consultations? What percent increase would be…
Two geysers that are near to each other are labelled as Geyser A and Geyser B. The time between eruptions for a given geyser follows an exponential distribution. The eruption times of the two geysers are independent of one another. The mean amount of time between eruptions of Geyser A is 39 minutes, and the mean amount of time between eruptions of Geyser B is 66 minutes. Given that exactly one of the geysers erupts within the next 49 minutes, determine the probability that it will be Geyser A. O 0.6654 0.7850 O 0.7252 O 0.6953 O 0.7551
Snapchat has more than 200 million daily users sending over 3 billion snaps a day. Suppose that: The time X between snaps you received is governed by: Exponential distribution, u = 8 minutes
The working life time, in years, of a particular model of electric oven is exponentially distributed with mean of 8. Find the 22th percentile of the working lifetime, in years.

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