Page 228 - DMTH404_STATISTICS

Statistics

Notes Normal probability distribution: The normal probability distribution occupies a place of central
importance in Modern Statistical Theory.
Binomial distribution: Normal distribution can be used as an approximation to binomial
distribution when n is large and neither p nor q is very small.

15.6 Self Assessment

1. ....................... distributions can be divided into two broad categories, viz. discrete and
continuous probability distributions, depending upon whether the random variable is
discrete or continuous.
(a) Theoretical probability (b) uniform distribution

(c) continuous random variable (d) normal probability distribution
2. A ....................... X is said to be uniformly distributed in a close interval
(a, b) with probability density function p(X) if

1
p X for a £ X £ b and
( ) =
b a
-
= 0 otherwise.
(a) Theoretical probability (b) uniform distribution

(c) continuous random variable (d) normal probability distribution
3. The ....................... is alternatively known as rectangular distribution.
(a) Theoretical probability (b) uniform distribution
(c) continuous random variable (d) normal probability distribution

4. The ....................... occupies a place of central importance in Modern Statistical Theory.
(a) Theoretical probability (b) uniform distribution
(c) continuous random variable (d) normal probability distribution
5. Normal distribution can be used as an approximation to ....................... when n is large and
neither p nor q is very small.
(a) Theoretical probability (b) uniform distribution
(c) continuous random variable (d) normal probability distribution

15.7 Review Questions

1. In a metropolitan city, there are on the average 10 fatal road accidents in a month (30 days).
What is the probability that (i) there will be no fatal accident tomorrow, (ii) next fatal
accident will occur within a week?
Hint : Take m = 1/3 and apply exponential distribution.
2. A counter at a super bazaar can entertain on the average 20 customers per hour. What is the
probability that the time taken to serve a particular customer will be (i) less than 5 minutes,
(ii) greater than 8 minutes?
Hint : Use exponential distribution.

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