(Hypergeometric and binomial Probability Distribution) Chapter 8
Q.1 a). The telephone company reports that among 5000 telephones installed in a new subdivision 4000 have push buttons. If 10 people are called at random what is the probability that exactly 3 will be talking on dial telephones?
b). Define hypergeometric distribution.
a) Let X denote the number of people that have dial telephones. probability of a push-button telephone is
b) HYPERGEOMETRIC DISTRIBUTION:
A probability distribution used to predict the outcome of a process in which different elements are randomly drawn from a collection and not replaced. For example, a hypergeometric distribution could be used to predict what color marble would be drawn from a jar if each marble drawn is not replaced.
Q.2) Define Bernoulli’s probability distribution.
An experiment in which a single action, such as flipping a coin, is repeated identically repeatedly. The possible results of the action are classified as “success” or “failure”. The binomial probability formula is used to find probabilities for Bernoulli trials.
In probability theory and statistics, the Bernoulli distribution, named after Swiss scientist Jacob Bernoulli, 1: is the probability of a random variable, which takes the value 1 with success probability of P and the value 0 with failure probability of q=i-p . It can be used to represent a coin toss where 1 and 0 would represent “head” and “tail” (or vice versa), respectively. In particular, unfair coins would have P is not equal to 0.5.
The Bernoulli distribution is a special case of the two-point distribution, for which the two possible outcomes need not be 0 and 1.
Q.3) If 5 cards are dealt from a standard deck of 52 playing cards what is the probability that 3 will be clubs.
Q.4) Prove that mean and variance of Bernoulli distribution is p and pq.
Q.6) The mean and variance of binomial distribution are 3 and 2, respectively. Find the probability that the variate takes values
i) less than or equal to 2
ii) greater than or equal to 7.
Q.9) Find the probabilities of the binomial experiment defined by n = 6 and p = 0.5.
Related: Statistics Chapter 5 (Index number)
Q.10) The probability of a man scoring a penalty in a Hockey match is 1/3. How many times he should be given a chance so that the probability of scoring successfully at least once is greater than ¾?
Q.11) If 30% of a population on their own homes, wheat is the probability that a sample of seven from the population will contain:
a) Exactly two homeowners?
b) At least five homeowners?
c) Exactly four homeowners?
Q.12) If the probability of getting defective items in a lot containing 200 items is 0.2, find the expected number of defective items in the lot and find its standard deviation.
Q.13) The output of a production process is 10% defective. What is the probability of selecting exactly two defectives in a sample of five?
Read more: Statistics-Chapter 3 (Measures of Location)
Q.14 a) Compute the mean and standard deviation for the binomial distribution for which p = 0.7 and n = 60.
b) Discuss the statement that is a binomial distribution n=5 and p=2.5.
c) The mean and variance of a binomial distribution are 42 and 12.6 respectively. Find p and n.
d) Is it possible to have binomial distribution with mean=5 and S.D=3?
Since p is greater than one so binomial distribution does not exist: