Draw a normal curve with μ = 140 and σ = 10. Label the mean and the inflection points.
Answer (2)
The problem provides a normal distribution with mean μ = 140 and standard deviation σ = 10 .
Inflection points are calculated as μ − σ = 130 and μ + σ = 150 .
The correct normal curve should be centered at 140 with inflection points at 130 and 150.
Option D correctly represents the normal curve with the specified mean and inflection points, so the answer is D .
Explanation
Understanding the Problem We are given a normal distribution with a mean ( μ ) of 140 and a standard deviation ( σ ) of 10. Our goal is to identify the correct normal curve that represents this distribution, with the mean and inflection points accurately labeled.
Calculating Inflection Points For a normal distribution, the inflection points are located at one standard deviation away from the mean, i.e., at μ − σ and μ + σ . Let's calculate these values:
Lower Inflection Point μ − σ = 140 − 10 = 130
Upper Inflection Point μ + σ = 140 + 10 = 150
Identifying the Correct Curve Therefore, the inflection points are at 130 and 150. We need to choose the option that shows a normal curve centered at 140 with inflection points at 130 and 150.
Selecting the Correct Option Option D shows a normal curve centered at 140 with inflection points at 130 and 150.
Final Answer The correct answer is D.
Examples
Normal distributions are incredibly useful in many real-world scenarios. For instance, in manufacturing, the weights of products often follow a normal distribution. If a company knows the mean and standard deviation of the weights, they can predict how many products will fall within a certain weight range. This helps them ensure quality control and avoid shipping products that are too heavy or too light. Understanding normal distributions allows businesses to make informed decisions and maintain consistent product standards.
To draw a normal curve with mean 140 and standard deviation 10, plot the mean at 140 and the inflection points at 130 and 150. Draw a symmetric bell-shaped curve centered at the mean, illustrating the normal distribution. Make sure to label the mean and inflection points appropriately.
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