Problem

Use the empirical probability formula to solve the exercise. Express the answer as a fraction. Then express the probability as a decimal, rounded to the nearest thousandth, if necessary.

In 1999 the stock market took big swings up and down. A survey of 1,015 adult investors asked how often they tracked their portfolio. The table shows the investor responses. What is the probability that an adult investor tracks his or her portfolio daily?
\begin{tabular}{l|l}
How frequently? & Response \\
\hline Daily & 233 \\
\hline Weekly & 286 \\
\hline Monthly & 296 \\
\hline Couple times a year & 145 \\
\hline Don't track & 55
\end{tabular}
$\frac{145}{1,015} ; 0.143$
$\frac{233}{1,015} ; 0.23$
$\frac{286}{1,015} ; 0.282$
$\frac{296}{1,015} ; 0.292$

Answer

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Answer

\(\boxed{\text{Final Answer: The probability that an adult investor tracks his or her portfolio daily is }\frac{233}{1015}\text{ or approximately }0.230\text{ when rounded to the nearest thousandth.}}\)

Steps

Step 1 :The problem provides a table of responses from a survey of 1,015 adult investors on how frequently they track their portfolio. The table shows the number of investors who track their portfolio daily, weekly, monthly, a couple of times a year, and those who don't track at all.

Step 2 :We are asked to find the probability that an adult investor tracks his or her portfolio daily. The probability of an event is calculated by dividing the number of ways the event can occur by the total number of outcomes.

Step 3 :In this case, the event is an investor tracking their portfolio daily, and the total number of outcomes is the total number of investors surveyed.

Step 4 :The number of investors who track their portfolio daily is given as 233, and the total number of investors surveyed is 1,015. So, the probability can be calculated by dividing 233 by 1,015.

Step 5 :Using the formula for empirical probability, we get \(\frac{233}{1015}\).

Step 6 :This gives us a decimal number. To express it as a fraction, we can simply write it as the ratio of the number of daily trackers to the total number of investors.

Step 7 :To express it as a decimal rounded to the nearest thousandth, we can round the decimal number obtained from the calculation to three decimal places.

Step 8 :Doing this, we find that the probability that an adult investor tracks his or her portfolio daily is approximately 0.230 when rounded to the nearest thousandth.

Step 9 :\(\boxed{\text{Final Answer: The probability that an adult investor tracks his or her portfolio daily is }\frac{233}{1015}\text{ or approximately }0.230\text{ when rounded to the nearest thousandth.}}\)

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