1. A fire department in a rural county reports that its response time to fires is approximately Normally distributed with a mean of 22 minutes and a standard deviation of 3.9 minutes. (a) Make an accurate sketch of the distribution of response time. (b) Use the empirical rule (68 - 95 - 99.7) to find the proportion of response times between 14.2 and 29.8 minutes (c) Calculate and interpret the 80th percentile of the distribution of response times. (d) The national mean response time is 18.5 minutes. What proportion of all response times for this fire department are below the national mean response time?
Added by Lynn H.
Close
Step 1
- Mean (\(\mu\)) = 22 minutes - Standard deviation (\(\sigma\)) = 3.9 minutes Show more…
Show all steps
Your feedback will help us improve your experience
Kari Hasz and 82 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Fire department response time is the length of time it takes a fire truck to arrive at the scene of a fire, starting from the time the call was given to the truck. The response time for the Castle Wood Fire Department follows a mound-shaped and symmetrical distribution. The response time has a mean μ = 8.8 minutes with a standard deviation σ = 2.1 minutes. If a random sample of 32 response times is taken and the mean response time x̄ is computed, find each of the following. A) P(x̄ ≥ 9) B) P(8 ≤ x̄ ≤ 9)
Shaiju T.
Fire department response time is the length of time it takes a fire truck to arrive at the scene of a fire starting from the time the call was given to the truck. Response time for the Castle Wood Fire Department follows a mound shaped and symmetrical distribution. The response time has mean μ = 8.8 minutes with standard deviation σ = 2.1 minutes. If a random sample of 32 response times is taken and the mean response time x̄ is computed, find each of the following. a. P(x̄ ≥ 9) b. P(8 ≤ x̄ ≤ 9)
Sri K.
Find the range, variance, and standard deviation for the given sample data. Include appropriate units (such as "minutes") in your results. (The same data were used in Section 3-I, where we found measures of center. Here we find measures of variation.) Then answer the given questions. Listed below are the numbers of heroic firefighters who lost their lives in the United States each year while fighting forest fires. The numbers are listed in order by year, starting with the year $2000 .$ What important feature of the data is not revealed by any of the measures of variation? $$\begin{array}{cccccccccccccc} 20 & 18 & 23 & 30 & 20 & 12 & 24 & 9 & 25 & 15 & 8 & 11 & 15 & 34 \end{array}$$
Describing, Exploring, and Comparing Data
Measures of Variation
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD