Question

the graph shows the normal curve describing the distribution of the heights of 10 - story buildings from cities around the world. what is the probability that a 10 - story building is shorter than 31 meters? (7 points)

Explanation:

Step1: Analyze the normal distribution properties

In a normal distribution, about 68% of the data lies within \( \mu\pm\sigma\), 95% within \( \mu\pm2\sigma\), and 99.7% within \( \mu\pm3\sigma\). The mid - point (mean \(\mu\)) of the given normal distribution is 33m. The distance from 33m to 29m is \(33 - 29=4\)m, and from 33m to 37m is also 4m. So, \(\sigma = 4\)m.

Step2: Calculate the probability for \(x < 29\)

The total area under the normal curve is 1 (or 100%). The area between \(29\)m and \(37\)m (\(\mu\pm\sigma\)) is 68%. So the area outside \(29\)m and \(37\)m is \(100\% - 68\%=32\%\). Since the normal distribution is symmetric, the area to the left of \(29\)m is \(\frac{100\% - 68\%}{2}=16\%\)

Answer:

16%