At the music store Katelyn bought 2 packs of
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Answer: Normal approximation can be used for discrete sampling distributions, such as Binomial distribution and Poisson distribution if certain conditions are met.
Step-by-step explanation: We will give conditions under which the Binomial and Poisson distribitions, which are discrete, can be approximated by the Normal distribution. This procedure is called normal approximation.
1. Binomial distribution: Let the sampling distribution be the binomial distribution , where
is the number of trials and
is the probability of success. It can be approximated by the Normal distribution with the mean of
and the variance of
, denoted by
if the following condition is met:
2. Poisson distribution: Let the sampling distribution be the Poisson distribution where
is its mean. It can be approximated by the Normal distribution with the mean
and the variance
, denoted by
when
is large enough, say
(however, different sources may give different lower value for
but the greater it is, the better the approximation).
The ratio X/Y for the fictitious company, Teslala, that produces a single type of electronic vehicle, Model Z is 10/pY.
<h3>What is a mathematical model?</h3>A mathematical model is the model which is used to explain the any system, the effect of the components by study and estimate the functions of systems.
Consider a fictitious company, Teslala, that produces a single type of electronic vehicle, Model Z.
The demand for Model Z depends on the gasoline price (q) because customers tend to purchase an electronic vehicle as a substitute for vehicles that run on gasoline when the gasoline price increases.
The demand for Model Z is estimated as
Here, <em>p</em> is the price of Model Z.
Consider the following two statements:
- 1. When the average gasoline price q increases by $1, the revenue-maximizing price p" increases by $X.
- 2. When the average gasoline price q increases by $1, the demand at the revenue-maximizing price (i.e., D(p*)) increases by a factor of Y.
Put the value of demand at the revenue-maximizing price as,
Thus, the ratio X/Y for the fictitious company, Teslala, that produces a single type of electronic vehicle, Model Z is 10/pY.
Learn more about the mathematical model here;
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