The paper "Parametric and Nonparametric Statistical Procedures" is a wonderful example of medical research. According to Heath (2002), a binomial distribution occurs if every trial has 2 likely and mutually exclusive outcomes. This applies when the consecutive trials are independent of each other. The fundamental rule that defines the binomial distribution is that each one of p independent outcomes is random and that each of the outcomes can be categorized in one of the two mutually exclusive groups. In a binomial distribution, the probability that an outcome will fall in group one is equal top, and the probability that the outcome will fall in group two is q.
Given that p + q = 1, it can thus be derived that 1 – p = q (Sheskin, 2000). From this concept, questions 3, 4, and 27 can thus be solved using the different methods used to calculate probability. The two methods used to calculate these questions are by listing all the possible outcomes and by using the binomial table (Steinberg, 2010). Practice 3 The number of children is 4. The probability of fathering a boy (B) or a girl (G) is 0.50 and 0.50 respectively.
Using the list and calculation method, calculate the probability. In this case, a hit is regarded as fathering a boy. Number of hits Number of ways Probability for the number of hits 0 hits 1 0.0625 1 hit 2 0.125 2 hit 2 0.125 3 hits 2 0.125 4 1 0.0625 Hence, the probability that exactly two will be boys is 0.125 The probability that fewer than two will be boys is 0.125 + 0.0625 = 0.1875 The probability that more than one will be a boy is 0.125 + 0.125 +0.0625 = 0.2125 Practice 4 3 cards are drawn with replacement.
Red is regarded as a hit. Number of hits Number of ways Probability of number of hits 0 hits 1 0.125 1 hit 3 0.375 2 hits 3 0.375 3 hits 1 0.125 Hence, the probability one will be red is 0.375 The probability none will be red is 0.125 The probability of more than two will be red is 0.125 Practice 27 There were five questions on the test and each question had 5 multiple answers from which Suzie had to choose. What was the probability that Suzie got at least 80% of the pop quiz? The probability of getting a question right on a five-choice selection through guesswork is 1/5, which is 0.20.
There were 5 questions, hence, N is 5. From the 0.20 column of the table where N is 5, the probability that Suzie got at least 80% of the pop quiz correct by guesswork is: 1− 0.9997 = 0.0003 Thus, the probability that Suzie got at least 80% of the pop quiz is less than one. Which means it is unlikely.
Heath, D. (2002). An Introduction To Experimental Design And Statistics For Biology. CRC Press.
Sheskin, D. (2000). Handbook of Parametric and Nonparametric Statistical Procedures (2nd ed.). Chapman & Hall/CRC Press.
Steinberg, W. J. (2010). Statistics Alive! SAGE.