SOLUTION: The weights of a certain dog breed are approximately normally distributed with a mean of 52 pounds, and a standard deviation of 6.6 pounds. Use your graphing calculator to answer t
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Question 1170928: The weights of a certain dog breed are approximately normally distributed with a mean of 52 pounds, and a standard deviation of 6.6 pounds. Use your graphing calculator to answer the following questions. Write your answers in percent form. Round your answers to the nearest tenth of a percent.
a) Find the percentage of dogs of this breed that weigh less than 52 pounds. %
b) Find the percentage of dogs of this breed that weigh less than 49 pounds. %
c) Find the percentage of dogs of this breed that weigh more than 49 pounds. %
Answer by CPhill(1959) (Show Source): You can put this solution on YOUR website!
Let's solve this problem using the properties of a normal distribution and a graphing calculator.
**Understanding the Problem**
* We have a normal distribution.
* Mean (μ) = 52 pounds
* Standard deviation (σ) = 6.6 pounds
**Using a Graphing Calculator**
We'll use the `normalcdf` function:
* `normalcdf(lower_bound, upper_bound, mean, standard_deviation)`
**Calculations**
**a) Percentage of dogs weighing less than 52 pounds**
* We want P(X < 52).
* `lower_bound`: -1E99 (or a very small number)
* `upper_bound`: 52
* `mean`: 52
* `standard_deviation`: 6.6
* `normalcdf(-1E99, 52, 52, 6.6)`
* Result: approximately 0.5
* Percentage: 0.5 \* 100% = 50.0%
**b) Percentage of dogs weighing less than 49 pounds**
* We want P(X < 49).
* `lower_bound`: -1E99 (or a very small number)
* `upper_bound`: 49
* `mean`: 52
* `standard_deviation`: 6.6
* `normalcdf(-1E99, 49, 52, 6.6)`
* Result: approximately 0.32044
* Percentage: 0.32044 \* 100% ≈ 32.0%
**c) Percentage of dogs weighing more than 49 pounds**
* We want P(X > 49).
* `lower_bound`: 49
* `upper_bound`: 1E99 (or a very large number)
* `mean`: 52
* `standard_deviation`: 6.6
* `normalcdf(49, 1E99, 52, 6.6)`
* Result: approximately 0.67956
* Percentage: 0.67956 \* 100% ≈ 68.0%
**Answers**
* a) 50.0%
* b) 32.0%
* c) 68.0%
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