The police reported that the average driver exceeds the 50 miles per hour speed limit by more than 9 miles per hour on the busiest street in a small town. A sample of 63 randomly selected cars were clocked by airplane radar. The average speed was 57.5 miles per hour, and the standard deviation of the speeds was 4.17 miles per hour. Determine if the average speed is greater than what the police department reported. Which parameter(s) are you given? Mark all that apply. p μ σ none Which statistic(s) are you given? Mark all that apply. ¯x ˆp ˆq s x none What is the problem asking you to do? Estimate a parameter Test a given parameter
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
The police reported that the average driver exceeds the 50 miles per hour speed limit by more than 9 miles per hour on the busiest street in a small town. A sample of 63 randomly selected cars were clocked by airplane radar. The average speed was 57.5 miles per hour, and the standard deviation of the speeds was 4.17 miles per hour. Determine if the average speed is greater than what the police department reported.
- Which parameter(s) are you given? Mark all that apply.
- p
- μ
- σ
- none
- Which statistic(s) are you given? Mark all that apply.
- ¯x
- ˆp
- ˆq
- s
- x
- none
- What is the problem asking you to do?
- Estimate a parameter
- Test a given parameter
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