a. What is the distribution of X? X- U b. Suppose that 36 people are surveyed. What is the distribution of a for this sample? - N c. What is the probability that the average birth month of the 36 people will be more than 5.8?
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!
![Treat the number of months X after January 1 that someone is born as uniformly distributed from 0 to 12.
Round all answers to 4 decimal places where possible.
a. What is the distribution of X? X- U
b. Suppose that 36 people are surveyed. What is the distribution of for this sample? - N(
C. What is the probability that the average birth month of the 36 people will be more than 5.8?
Hint:
Some Helpful Videos:
• Finding the Sampling Distribution [+]
Finding a Probability Using the Central Limit Theorem [+]
Finding Value Given a Probability Using the Central Limit Theorem [+]
• The Central Limit Theorem For Sums [+]
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