1) For each scenario listed below an inspector at the TechKnow company has a que
ID: 1848581 • Letter: 1
Question
1) For each scenario listed below an inspector at the TechKnow company has a question that can be answered with a probability distribution. Say whether the distribution is most likely to be
Normal
Lognormal
Weibull
Gamma
Beta
Exponential
(as an added hint each distribution is used exactly once)
a) A-An inspector knows if he can find more than 10 defective microchips at the TechKnow company then he can shut them down. He wondering how long it will take for him to find 10 defective chips
b) B- When a computer is loaded for the first time it has to load several components at the same time (thanks to multiple processors). The inspector waits until every component has finished loading. He wonders how long it will take the next computer to load
c) C-The employee roster at TechKnow has been experiencing the same slow increase as the rest of the company. The inspector wonders how many other companies have as many employees as TechKnow
d) D-The electrical voltage through a microchip is supposed to be exactly 0.11 volts. If it is over 0.114 the chip will fry. The inspector wonders how likely the nextchip is to get fried by over voltage
e) E- The inspector grabs a box of 250 microchips. He wonders if this box will have 10 defective chips
f) F- He will plan his lunch break for when he finds his first defective chip. He
Explanation / Answer
The normal distribution, also called Gaussian distribution, is an extremely important probability distribution in many fields. It is a family of distributions of the same general form, differing in their location and scale parameters: the mean ("average") and standard deviation ("variability"), respectively. The standard normal distribution is the normal distribution with a mean of zero and a standard deviation of one (the green curves in the plots to the right). It is often called the bell curve because the graph of its probability density resembles a bell In probability theory and statistics, the beta distribution is a family of continuous probability distributions defined on the interval [0, 1] parametrized by two positive shape parameters, denoted by a and ß. The beta distribution has been applied to model the behavior of random variables limited to intervals of finite length in a wide variety of disciplines. Some examples follow. In population genetics it has been employed for a statistical description of the allele frequencies in the components of a sub-divided population[1] . It has been utilized in PERT[2], critical path method (CPM) and other project management / control systems to describe the statistical distributions of the time to completion and the cost of a task. It has been applied in acoustic analysis to assess damage to gears, as the kurtosis of the beta distribution has been reported as a good indicator of the condition of gears.[3] It was used to model sunshine data for application to solar renewable energy utilization.[4] It has been utilized for parametrizing variability of soil properties at the regional level for crop yield estimation, modeling crop response over the area of the association.[5] It was selected to determine well-log shale parameters, to describe the proportions of the mineralogical components existing in a certain stratigraphic interval.[6] Heterogeneity in the probability of HIV transmission in heterosexual contact has been modeled as a random variable in a beta distribution, and parameters estimated by maximum-likelihood[7] . In Bayesian inference, beta distributions provide a family of conjugate prior probability distributions for binomial and geometric distributions. For example, the beta distribution can be used in Bayesian analysis to describe initial knowledge concerning probability of success such as the probability that a space vehicle will successfully complete a specified mission. The beta distribution is a suitable model for the random behavior of percentages and proportions. One theoretical case where the beta distribution arises is as the distribution of the ratio formed by one random variable having a Gamma distribution divided by the sum of it and another independent random variable also having a Gamma distribution with the same scale parameter (but possibly different shape parameter). The usual formulation of the beta distribution is also known as the beta distribution of the first kind, whereas beta distribution of the second kind is an alternative name for the beta prime distribution.
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