Question

Probabilities and areas under a curve

Discuss why probabilities for the normal distribution and other continuous distributions are the same as areas under the curve for a given interval.

Answer 1

answer:

Probability and the Normal Curve:

• The normal distribution is a continuous probability distribution.
• This has several implications for probability.
• The total area under the normal curve is equal to 1.
• The probability that a normal random variable X equals any particular value is 0.
• The probability that X is greater than a equals the area under the normal curve bounded by a and plus infinity (as indicated by the non-shaded area in the figure below).
• The probability that X is less than a equals the area under the normal curve bounded by a and minus infinity (as indicated by the shaded area in the figure below).
  

Discuss why probabilities for the normal distribution and other continuous distributions are the same as areas under the curve for a given interval:

• Territory under the bend, y = f(x) for a given interim, state [a, b] is
• Fundamental 'a to b'of {f(x)dx} .....(1)
• On the off chance that the pdf of a persistent variable, X is given by f(x), at that point P(a < X < b) is
• Vital 'a to b'of {f(x)dx} ....(2)
• (1) and (2) => probabilities for the typical circulation and different persistent disperasions are equivalent to regions under the bend for a given interim.