The birthrates in the United States for the year 2003-2012 are given i

korporasidn

korporasidn

Answered question

2021-12-04

The birthrates in the United States for the year 2003-2012 are given in the following table. (The birthrate is the number of live births/1000 population.)
Year20032004200520062007Birthrate14.714.014.014.214.2
Year20082009201020112012Birthrate14.013.813.813.813.7
a. Describe a random variable X that is associated with these data.
b. Find the probability distribution for the random variable X.
c. Compute the mean, variance, and standard deviation of X.

Answer & Explanation

Novembruuo

Novembruuo

Beginner2021-12-05Added 26 answers

Step 1
a. The random variable X is the annual birth rate during the years 2003−2012.
Step 2
b. Total number of outcomes is 10.
The birth rate 14.7 occurs 1 time.
The birth rate 14.0 occurs 3 times.
The birth rate 14.2 occurs 2 times.
The birth rate 13.8 occurs 3 times.
The birth rate 13.7 occurs 1 time.
The probability distribution table is shown below:
Birth rateProbabilityP(X)13.71/100.113.83/100.314.02/100.213.71/100.113.83/100.3
Step 3
c. The required calculations for obtaining mean, variance and standard deviation are made in the following table:
XP(X)X.P(X)X2X2P(X)13.70.11.37187.6918.76913.80.34.14190.4457.13214.00.22.819639.213.70.11.37187.6918.76913.80.34.14190.4457.132Total1.0013.82952.26191.002
Step 4
The expected value is calculated as follows:
μ=SXP(X)
=13.82
The mean is 13.82.
The variance is calculated as follows:
Variance=X2P(X)E(X)2
=191.002(13.82)2
=0.0096
Thus, the variance is 0.0096.
Standard deviation=variance=0.0096=0.0980.

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