Question

a survey of 685 people showed that 433 had a group health insurance plan where they worked. based on this survey, what is the empirical probability that an employee has a group health insurance plan? write the answer as a percent rounded to the nearest tenth.

Explanation:

Step1: Recall the formula for empirical probability

Empirical probability \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). Here, the number of favorable outcomes (people with group health insurance) is \(n = 433\), and the total number of outcomes (total people surveyed) is \(N=685\). So, \(P=\frac{433}{685}\).

Step2: Calculate the decimal value

\(\frac{433}{685}\approx0.632117\).

Step3: Convert the decimal to a percentage

To convert a decimal to a percentage, multiply by \(100\). So, \(0.632117\times100 = 63.2117\%\).

Step4: Round to the nearest tenth

Rounding \(63.2117\%\) to the nearest tenth. Look at the second - decimal digit (1). Since \(1\lt5\), we keep the first - decimal digit as it is.

Answer:

\(63.2\%\)