Compute P(X) using the binomial probability formula. Then determine whether the normal distribution can be used to estimate this probability. If so, approximate P(X) using the normal distribution and compare the result with the exact probability.n=56 p=0.5 x=30 A)For n=56, p=0.5, and X=30, use the binomial probability formula to find P(X). B)Can the normal distribution be used to approximate this probability?A.No, because np(1−p)≤10 B.Yes, because np(1−p)≥10 C.Yes, because np(1−p)≥10 D.No, because np(1−p)≤10 C)Approximate P(X) using the normal distribution. Use a standard normal distribution table.A.P(X)=enter your response here(Round to four decimal places as needed.) B.The normal distribution cannot be used. D)By how much do the exact and approximated probabilities differ?A.enter your response here(Round to four decimal places as needed.)B.The normal distribution cannot be used. E)By how much do the exact and approximated probabilities differ?

It is given that X follows Binomial(n = 56, p = 0.5), then the probability function P(X = x) =…

Answered: A)For n=56, p=0.5, and X=30, use the…

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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Compute P(X) using the binomial probability formula. Then determine whether the normal distribution can be used to estimate this probability. If so, approximate P(X) using the normal distribution and compare the result with the exact probability.

n=56 p=0.5 x=30

A)For n=56, p=0.5, and X=30, use the binomial probability formula to find P(X).

B)Can the normal distribution be used to approximate this probability?

No, because np(1−p)≤10

Yes, because np(1−p)≥10

No, because np(1−p)≤10

Approximate P(X) using the normal distribution. Use a standard normal distribution table.

P(X)=enter your response here

(Round to four decimal places as needed.)

The normal distribution cannot be used.

By how much do the exact and approximated probabilities differ?

A.enter your response here

(Round to four decimal places as needed.)

The normal distribution cannot be used.

E)By how much do the exact and approximated probabilities differ?

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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