can you explain in detail According to the report about the survey performed by Company XYZ that 60% of the people think that violence has increased in theoast 4 years. In a future random sample of 250 people in a certain age of more 20 years old group, if we let X be the number of suchpeople in that sample who think that the proposal is correct.a) What is the approximate distribution of X with parameters? Provide your explanation in the answer box below. If nothing has beenput forth as an explanation, you will not receive a grade.b) Find P (120 sXs 200) Explain why an approximate probability that X is between 120 and 200 both inclusive.c) Find probability that X is at most 130.

Answered: According to the report about 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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can you explain in detail

According to the report about the survey performed by Company XYZ that 60% of the people think that violence has increased in the
oast 4 years. In a future random sample of 250 people in a certain age of more 20 years old group, if we let X be the number of such
people in that sample who think that the proposal is correct.
a) What is the approximate distribution of X with parameters? Provide your explanation in the answer box below. If nothing has been
put forth as an explanation, you will not receive a grade.
b) Find P (120 sXs 200) Explain why an approximate probability that X is between 120 and 200 both inclusive.
c) Find probability that X is at most 130.

Expert Solution

Step 1

The given scenario follows binomial distribution as the sample size is large, np and nq are also greater than 5, it can be approximated to a normal distribution.

That is,

Thus, the normal approximation for binomial distribution can be used.

The mean and standard deviation of the normal distribution is,

Thus, the mean and standard deviation of the distribution is 150 and 7.75 respectively.

Therefore, the random variable X approximately follows normal distribution with mean as 150 and standard deviation as 7.75.

Step 2

Using the correction for continuity the probability that the random variable X is between 120 and 200 inclusively is,

Thus, the probability that the random variable X is between 120 and 200 inclusively is 0.99996.

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