Question

the accompanying data represent the ideal number of children for a random sample of 900 adults. complete parts (a) through (d) below. click the icon to view the data about ideal numbers of children. (a) construct a discrete probability distribution for the random variable x. (round to three decimal places as needed.)

Explanation:

Step1: Recall the formula for probability

The probability \(P(x)\) of a discrete random variable \(x\) is given by \(P(x)=\frac{\text{Frequency of }x}{\text{Total number of observations}}\). Here, the total number of observations \(n = 900\).

Step2: Calculate \(P(0)\)

For \(x = 0\), frequency \(f=9\). Then \(P(0)=\frac{9}{900}=0.010\)

Step3: Calculate \(P(1)\)

For \(x = 1\), frequency \(f = 29\). Then \(P(1)=\frac{29}{900}\approx0.032\)

Step4: Calculate \(P(2)\)

For \(x = 2\), frequency \(f = 532\). Then \(P(2)=\frac{532}{900}\approx0.591\)

Step5: Calculate \(P(3)\)

For \(x = 3\), frequency \(f = 240\). Then \(P(3)=\frac{240}{900}\approx0.267\)

Step6: Calculate \(P(4)\)

For \(x = 4\), frequency \(f = 70\). Then \(P(4)=\frac{70}{900}\approx0.078\)

Step7: Calculate \(P(5)\)

For \(x = 5\), frequency \(f = 17\). Then \(P(5)=\frac{17}{900}\approx0.019\)

Step8: Calculate \(P(6)\)

For \(x = 6\), frequency \(f = 3\). Then \(P(6)=\frac{3}{900}=0.003\)

Answer:

\(x\) (\(\#\) of children)	\(P(x)\)
\(1\)	\(0.032\)
\(2\)	\(0.591\)
\(3\)	\(0.267\)
\(4\)	\(0.078\)
\(5\)	\(0.019\)
\(6\)	\(0.003\)