At Westonci.ca, we make it easy to get the answers you need from a community of informed and experienced contributors. Discover in-depth solutions to your questions from a wide range of experts on our user-friendly Q&A platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
Answer:
The approximate proportion of 1-mile long roadways with potholes numbering between 20 and 70 is 0.9735.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 50, standard deviation = 10.
Between 20 and 70.
The normal distribution is symmetric, which means that 50% of the measures are below the mean and 50% are above.
20
20 = 50 - 3*10
So 20 is 3 standard deviations below the mean. Of the 50% of the measures below the mean, 99.7% are within 3 standard deviations of the mean, that is, above 20.
70
70 = 50 + 2*10
So 70 is 2 standard deviations above the mean. Of the 50% of the measures above the mean, 95% are within 2 standard deviations of the mean, that is, below 70.
Percentage:
0.997*50% + 0.95*50% = 97.35%
As a proportion, 97.35%/100 = 0.9735.
The approximate proportion of 1-mile long roadways with potholes numbering between 20 and 70 is 0.9735.
We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.
