We appreciate your visit to According to a website the mean weight of an adult member of a particular breed of dog is 148 pounds Assume the distribution of weights. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
Final answer:
The standard score for a weight of 164 pounds is 2.286. The probability that a randomly selected dog of this breed weighs more than 164 pounds is approximately 2.28%. Almost all adult dogs of this breed will weigh 134 pounds and 162 pounds.
Explanation:
To find the standard score associated with a weight of 164 pounds, we can use the formula z = (x - μ) / σ, where x is the weight, μ is the mean, and σ is the standard deviation. Plugging in the values, we get z = (164 - 148) / 7 = 2.286.
Using the Empirical Rule, we know that approximately 68% of the data falls within one standard deviation of the mean. Since the weight of 164 pounds is more than one standard deviation above the mean, the probability that a randomly selected dog of this breed weighs more than 164 pounds is less than 68%.
Using technology, we can confirm the exact probability. By calculating the area under the Normal distribution curve to the right of 164, we find that the probability is approximately 0.0228 or 2.28%.
Almost all adult dogs of this breed will have weights between the mean minus two standard deviations and the mean plus two standard deviations. Therefore, the weights will be between 148 - (2 * 7) = 134 pounds and 148 + (2 * 7) = 162 pounds.
Learn more about Normal distribution here:
https://brainly.com/question/34741155
#SPJ2
Thanks for taking the time to read According to a website the mean weight of an adult member of a particular breed of dog is 148 pounds Assume the distribution of weights. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
Final answer:
We first calculate the z-score by determining how many standard deviations far from the mean the value of 164 pounds is. Then using the Empirical Rule, we determine that around 15.85% of dogs weigh above 164 pounds. Confirming these calculations using a specific calculator will give us an accurate value, which can be used to indicate the range for the weights of almost all adult dogs.
Explanation:
Standard score, also known as a z-score, helps in understanding the data point's relationship to the mean of a group of data. To calculate the z-score for the weight of 164 pounds:
Z = (Sample Mean - Population Mean)/Standard Deviation = (164 - 148)/pounds.
The Empirical Rule, also known as the 68-95-99.7 rule, states that for a normal distribution: approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations. Therefore, if we learn that the z-score is 1 (for the example), it implies that the weight 164 pounds is one standard deviation above the mean. Considering the Empirical Rule, it would mean that approximately 15.85% of dogs have a weight over 164 pounds as it's the part of the 32% of data that lies above the mean.
Using computing software or a specific calculator, we can input the normal distribution parameters to confirm these calculations and then use it to calculate the range in which almost all adult dogs' weights fall.
Learn more about Statistics here:
https://brainly.com/question/31538429
#SPJ11
