distribution

• Binomial distribution


  If every outcome of an experiment can be classified as either a success or failure and the probability of success is denoted by p while the probability of failure is 1-p where p+1-p=1, then the experiment is said to be a binomial distribution
• Binomial distribution


  • Is an experiment that results in two outcomes
• Binomial experiment


  When an experiment is performed in a sequence of n independent and identical Bernoulli trials, then the experiment is called a binomial experiment
• Binomial experiment properties


  • The experiment consists of n repeated trials
  • Each trial is a Bernoulli trial
  • The trials are independent
  • The probability p of success and the probability 1-p of failure are constant for each trial
• Example 1


  • A six-sided die is rolled 12 times. What is the probability of getting a 4 five times?
• Example 2


  • A multiple choice test contains 20 questions with answer choices A, B, C, and D. Only one answer choice to each question represents a correct answer. Find the probability that a student will answer exactly 6 questions correct if he makes random guesses on all 20 questions.
• Example 3


  • A small business receives, on average, 12 customers per day. What is the probability that the business will receive exactly 8 customers in one day?
• Example 4


  • The average number of cellphones sold by a store at Greenhills Shopping Center is three per day. What is the probability that exactly 4 cellphones will be sold tomorrow?
• Example 5


  • The average number of traffic accidents on a certain intersection in Manila is two per month. Find the probability that zero accidents happen on that certain intersection in a one month period.
• •The normal distribution is also know as Gaussian distribution, in honor of the renowned German Mathematician Johann Carl Friedrich Gauss who derived the equation of its probability density function.
• •Central Limit Theorem states that both the sum and the mean of many random variables defined by real-life quantities have approximately normal distribution.
• •The graph of the pdf of a normally distributed random variable X is a bell-shaped curve known as the normal curve.