8. The percent of persons (ages 5 and older) in
Terrance Khan
Answered question
2022-02-11
Answer & Explanation
Jack Hobbs
Beginner2022-02-12Added 14 answers
X=(The percent of persons (ages 5 and older) in each state who speak a language at home other than Englis)
b. According to the provided information of the problem, the random variable X is exponentially distribution, hence the X will be continuous.
c. According to the provided information of the problem, the random variable X is exponentially distribution and can be defined as below:
=X~Exp(1/9.848)
=X~Exp(0.1015)
Where m=0.1015
d. The mean can be represented as below:
mu=9.948
Therefore, the mean is 9.848. e. The standard deviation can be calculated as below:
sigma=mu
=9.848
Therefore, the standard is 9.848.
f. It is given that X~Exp(0.1015) so it clear that,
m=0.1015
And, the general form of probability density function of exponential distribution is given as below,
f(x)=me^(-mx)
So, put the value of m. Then,
f(x)=0.1015e^(-1015x)
Therefore, the above expression is representing the probability density function of this problem.
Now, make the graph by using the above obtained probability density function. The maximum value of f(x) which will lie on the y-axis and at x=0 will be:
f(0)=0.1015e^(10150*0)
= 0.1015e^0
= 0.1015
= m g. It is known that the cumulative distribution function of exponential distribution is,
P(X<x)=1-e^(-mx)
Now, the required probability can be calculated as below:
P(x<12)=1-e^(-0.1015*12)
=1-0.2958
Therefore, the value of P(x<12) is 0.7042.
h. The required probability can be calculated as below:
P(8<x<14)=P(x<14)-P(x<8)
=1-e^(-0.1015*14)-(1-e^(-0.1015*8))
=0.4440-0.2415
=0.2025
Therefore, the value of P(8<x<14) os 0.2025
j. i. This sould be because the higher value of standard deviation which is present into the collected data.
ii. The given percentage is higher than 9.848 because there is huge chances that each state will have English speakers higher and lower than the mean percentage.
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