In binomial distribution n=8, 16 P (2) = P(6) find mean.
Answers
Answer:
Binomial Distribution
The mean of the distribution (μx) is equal to n * P .
The variance (σ2x) is n * P * ( 1 - P ).
The standard deviation (σx) is sqrt[ n * P * ( 1 - P ) ].
Step-by-step explanation:
Definition
Suppose a random experiment has the following characteristics.
There are n identical and independent trials of a common procedure.
There are exactly two possible outcomes for each trial, one termed “success” and the other “failure.”
The probability of success on any one trial is the same number p.
Then the discrete random variable X that counts the number of successes in the n trials is the binomial random variable with parameters n and p. We also say that X has a binomial distribution with parameters n and p.
The following four examples illustrate the definition. Note how in every case “success” is the outcome that is counted, not the outcome that we prefer or think is better in some sense.
A random sample of 125 students is selected from a large college in which the proportion of students who are females is 57%. Suppose X denotes the number of female students in the sample. In this situation there are n = 125 identical and independent trials of a common procedure, selecting a student at random; there are exactly two possible outcomes for each trial, “success” (what we are counting, that the student be female) and “failure;” and finally the probability of success on any one trial is the same number p = 0.57. X is a binomial random variable with parameters n = 125 and p = 0.57.
A multiple-choice test has 15 questions, each of which has five choices. An unprepared student taking the test answers each of the questions completely randomly by choosing an arbitrary answer from the five provided. Suppose X denotes the number of answers that the student gets right. X is a binomial random variable with parameters n = 15 and p=1∕5=0.20.
In a survey of 1,000 registered voters each voter is asked if he intends to vote for a candidate Titania Queen in the upcoming election. Suppose X denotes the number of voters in the