(i) Use normal approximation to a Binomial Distribution (X) having n=500 trials and p = 0.025 for finding out: a) P(X>10); (b) P(X<18) (c) P(X>21) (d) P(9
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!
- (i) Use normal approximation to a Binomial Distribution (X) having n=500 trials and p = 0.025 for finding out: a) P(X>10); (b) P(X<18) (c) P(X>21) (d) P(9<X<14)
(ii) If 1% of an airline’s flight suffers a minor equipment failure in an aircraft, what is the probability that there will be exactly 5 such in the next 1000 such flights?
(iii) During a laboratory experiment, the average number of radioactive particles passing through a counter in 1 millisecond is 2. What is the probability that 5 particles enter the counter in any given millisecond?
(iv) Records show that the probability is 0.000002 that a bike rider will have an accident while driving on the way of university through Biswamil. Using Poisson distribution determine the probability that among 200,000 bike riders driven on the way of university through Biswamil, not more than one will have an accident. ( e-0.4 = 0.67)
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