Which of the following are the properties of Normal Distribution function f(x) and Normal probability curve:
(A) The probability of success remains the same in each trial and the number of trials is small in number.
(B) The curve is bell shaped and is symmetrical about the mean.
(C) If set of n trials are repeated N times, then frequency $f(r)$ of $r$ successes is given by $f(r) = N.P(r) = Ne^{-m}.\frac{m^r}{r!},r=0,1,2,....$
(D) As x increases numerically, f(x) decreases rapidly and the maximum value of f(x) occurs at $x=μ$ (mean)
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (B) and (D) only
Properties of Normal Distribution and Normal Probability Curve:
(A) ❌ Not related to Normal Distribution (describes Binomial distribution properties)
(B) ✅ The curve is bell-shaped and symmetrical about the mean
(C) ❌ Describes Poisson distribution, not Normal distribution
(D) ✅ As $x$ moves away from the mean, $f(x)$ decreases rapidly, maximum at $x = \mu$
Answer: (B) and (D)