The average number of people who attend a soccer game at the Salt Lake Stadium in West Bengal, India is 64,286 and the standard deviation is 17,061. Assume the distribution of attendance at the Salt Lake Stadium is normal. Let X be the number of people who attend a soccer game at the Salt Lake Stadium at a randomly selected soccer game. Round all answers to 4 decimal places where possible. USing ti84 a. What is the distribution of X? X ~ N(,) b. Find the proportion of all games at the Salt Lake Stadium that have an attendance between 48,931 and 64,286 people. c. The 95th percentile for soccer game attendance at the Salt Lake Stadium is people. (Round to the nearest whole number)
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!
a. What is the distribution of X? X ~ N(,)
b. Find the proportion of all games at the Salt Lake Stadium that have an attendance between 48,931 and 64,286 people.
c. The 95th percentile for soccer game attendance at the Salt Lake Stadium is people. (Round to the nearest whole number)
d. The middle 70% of attendance at the Salt Lake Stadium will have from people to people. (Round to the nearest whole number)
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