Answer the following questions regarding the normal, standardnormal, and binomia

Question

Answer the following questions regarding the normal, standardnormal, and binomial distribution. a) how does the standardnormal distribution differ from thenormal distribution? b) what are the advantages of using the standard normaldistribution over normal distribution? c) Why is the correction of continuity necessary when thenormal distribution is used to approximate a binomialdistribution? Answer the following questions regarding the normal, standardnormal, and binomial distribution. a) how does the standardnormal distribution differ from thenormal distribution? b) what are the advantages of using the standard normaldistribution over normal distribution? c) Why is the correction of continuity necessary when thenormal distribution is used to approximate a binomialdistribution?

Explanation / Answer

(a) a standard normal distribution is a normaldistribution with mean 0 and variance 1, it is a special case ofnormal distribution, denoted by N(0,1).

a normal distribution couls have any value ofmean and variance, denoted by N(, ²), where ismean and ² is variance. A normal distribution can beconverted to a standard normal dsitribution by usingZ=(x-)/.

(b) We can compare different normal distributionwith different means and variance after tansforming them intostandard normal distributions. Also the probability table is readyfor standard normal distributions, so it is easy to find theprobability or z-score value.

(c) we use continuity correction because binomialis discrete distribution and normal distribution is continousdistribution. For example, To find P(X=2) in the normaldistribution. If you just use x =2 then the probability will bezero because with a continuous distribution the probability of anysingle value is zero. Therefore we have to use continuitycorrection to find P(1.5<x<2.5).

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