Question 1170930: The patient recovery time from a particular surgical procedure is normally distributed with a mean of 6 days and standard deviation of 1.7 days. 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) What is the probability of spending less than 6 days in recovery? %
b) What is the probability of spending more than 4 days in recovery? %
c) What is the probability of spending between 4 days and 6 days in recovery? %
Question Help Question 4: Video 1
Answer by CPhill(1987)   (Show Source):
You can put this solution on YOUR website! Here's how to solve this problem using the properties of a normal distribution:
**Understanding the Problem**
* We have a normal distribution.
* Mean (μ) = 6 days
* Standard deviation (σ) = 1.7 days
**Using a Graphing Calculator**
Most graphing calculators (like TI-84, etc.) have built-in functions to calculate probabilities for normal distributions. Here's the general process:
1. **Access the Normal Distribution Function:**
* Look for a "DISTR" or "Distribution" menu.
* Find "normalcdf" (normal cumulative distribution function).
2. **Input the Values:**
* `normalcdf(lower_bound, upper_bound, mean, standard_deviation)`
**Calculations**
**a) Probability of spending less than 6 days in recovery**
* We want P(X < 6), where X is the recovery time.
* `lower_bound`: A very small number (e.g., -1E99 or -10000) to represent negative infinity.
* `upper_bound`: 6
* `mean`: 6
* `standard_deviation`: 1.7
* `normalcdf(-1E99, 6, 6, 1.7)`
* The result will be approximately 0.5
* Percentage: 0.5 \* 100% = 50.0%
**b) Probability of spending more than 4 days in recovery**
* We want P(X > 4)
* `lower_bound`: 4
* `upper_bound`: A very large number (e.g., 1E99 or 10000)
* `mean`: 6
* `standard_deviation`: 1.7
* `normalcdf(4, 1E99, 6, 1.7)`
* The result will be approximately 0.88079
* Percentage: 0.88079 \* 100% ≈ 88.1%
**c) Probability of spending between 4 days and 6 days in recovery**
* We want P(4 < X < 6)
* `lower_bound`: 4
* `upper_bound`: 6
* `mean`: 6
* `standard_deviation`: 1.7
* `normalcdf(4, 6, 6, 1.7)`
* The result will be approximately 0.38079
* Percentage: 0.38079 \* 100% ≈ 38.1%
**Answers**
* a) 50.0%
* b) 88.1%
* c) 38.1%
|
|
|
