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 35 people are surveyed. What is the distribution of a for this sample? ī - N c. What is the probability that the average birth month of the 35 people will be more than 7.2?
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.
Given information:
The number of months X after January 1 that someone is born is uniformly distributed from 0 to 12.
It is required to obtain:
a. The distribution of X.
b. The distribution of for the sample of n = 35 people.
c. The probability that the average birth month of the people will be more than 7.2.
Introduction:
For a uniform random variable X, the probability density function is:
The mean and variance of a uniform random variable are respectively.
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
