There's a category of world-class runners that are known to run a marathon (26 miles) in an average of 143 minutes with a standard deviation of 14 minutes. Consider 49 of the races. X= the average of the 49 races 1. I need help with finding the probability that the average of the sample will be between 142 and 145 minutes in these 49 marathons. (the answer has to be rounded to four decimal places for it to be correct) 2. I also need help finding the 70th percentile for the average of these 49 marathons (the answer has to be rounded to two decimal places for it to be correct)
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!
There's a category of world-class runners that are known to run a marathon (26 miles) in an average of 143 minutes with a standard deviation of 14 minutes. Consider 49 of the races.
X= the average of the 49 races
1. I need help with finding the
2. I also need help finding the 70th percentile for the average of these 49 marathons (the answer has to be rounded to two decimal places for it to be correct)
Note: I would appreciate it if you could explain it step by step so I can see how you got the answer, thanks !
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 26 images
