Question

1) How is probability determined from a continuous distribution? Also, why is this easy for the uniform distribution and not so easy for the normal distribution? 2) What does the symmetry of the bell shape of the normal curve imply about the distribution of individuals in a normal population? 3) For a continuous probability density function, explain why P(a<x<b) = P(a≤x≤b).

Name: 1 how is probability determined from a continuous distribution also why is this easy for the uniform distribution and not so easy for the normal distribution 2 what does the symmetry of the 25097
Uploaded: 2023-05-10T08:54:36-08:00
Duration: 3 min 31 s
Channel: Madhur L
Description: 1 how is probability determined from a continuous distribution also why is this easy for the uniform distribution and not so easy for the normal distribution 2 what does the symmetry of the 25097

          1) How is probability determined from a continuous distribution? Also, why is this easy for the uniform distribution and not so easy for the normal distribution?
    2) What does the symmetry of the bell shape of the normal curve imply about the distribution of individuals in a normal population?
    3) For a continuous probability density function, explain why P(a<x<b) = P(a≤x≤b).

Added by Mitchell L.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Madhur L

05/10/2023

Step 1

For a continuous random variable X with PDF f(x), the probability that X lies in the interval [a, b] is given by: $$P(a \leq X \leq b) = \int_{a}^{b} f(x) dx$$ For the uniform distribution, this is easy because the PDF is a constant value, so the area under the Show more…

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1) How is probability determined from a continuous distribution? Also, why is this easy for the uniform distribution and not so easy for the normal distribution? 2) What does the symmetry of the bell shape of the normal curve imply about the distribution of individuals in a normal population? 3) For a continuous probability density function, explain why P(a<x<b) = P(a≤x≤b).