Question

When 430 randomly selected light bulbs were tested in a laboratory, 224 lasted more than 500 hours. Find a point estimate of the proportion of all light bulbs that last more than 500 hours.

Answer 1

To find the point estimate of the proportion of all light bulbs that last more than 500 hours, you can use the formula for the point estimate of a proportion:

\[
\hat{p} = \frac{x}{n}
\]

where:
- \(\hat{p}\) is the point estimate of the proportion,
- \(x\) is the number of successes (in this case, the number of light bulbs that lasted more than 500 hours), and
- \(n\) is the total number of trials (the total number of light bulbs tested).

Given:
- \(x = 224\) (the number of light bulbs that lasted more than 500 hours)
- \(n = 430\) (the total number of light bulbs tested)

Now, plug in the values:

\[
\hat{p} = \frac{224}{430}
\]

Calculating this:

\[
\hat{p} \approx 0.5209
\]

Thus, the point estimate of the proportion of all light bulbs that last more than 500 hours is approximately **0.5209** or **52.09%**.