Question
A normal distribution curve is titled Heights of 10-story building in meters. The horizontal axis ranges 27 to 39 in increments of 2. Corresponding vertical lines are drawn inside the curve from each value to the curve, creating defined regions.
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 35 meters?
(1 point)
Responses
84%
84%
16%
16%
15.85%
15.85%
50%
50%
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 35 meters?
(1 point)
Responses
84%
84%
16%
16%
15.85%
15.85%
50%
50%
Answers
GPT-4o mini
To determine the probability that a 10-story building is shorter than 35 meters from a normal distribution curve, we need to look at where 35 meters falls on the distribution.
Given that the horizontal axis ranges from 27 to 39 meters, and it is a normal distribution, we can infer the following:
1. If 35 meters is less than the mean of the distribution, the probability will be more than 50%.
2. If it is equal to the mean, then the probability will be 50%.
3. If it is above the mean, the probability would be lower than 50%.
Typically, in a normal distribution curve, about 84% of the values lie below one standard deviation above the mean. Since 35 meters is likely within this range and based on typical z-scores for a standard normal distribution, we can conclude that a significant proportion of the area under the curve is to the left of 35 meters.
Since we have options of 84%, 16%, 15.85%, and 50%, the closest probability that corresponds to being below 35 meters when interpreting the standard normal distribution would be:
**84%**
So the probability that a 10-story building is shorter than 35 meters is **84%.**
Given that the horizontal axis ranges from 27 to 39 meters, and it is a normal distribution, we can infer the following:
1. If 35 meters is less than the mean of the distribution, the probability will be more than 50%.
2. If it is equal to the mean, then the probability will be 50%.
3. If it is above the mean, the probability would be lower than 50%.
Typically, in a normal distribution curve, about 84% of the values lie below one standard deviation above the mean. Since 35 meters is likely within this range and based on typical z-scores for a standard normal distribution, we can conclude that a significant proportion of the area under the curve is to the left of 35 meters.
Since we have options of 84%, 16%, 15.85%, and 50%, the closest probability that corresponds to being below 35 meters when interpreting the standard normal distribution would be:
**84%**
So the probability that a 10-story building is shorter than 35 meters is **84%.**