Homework #4-Chapter13 (20pts for turned in on time) 1. (10pts) Binomial I distri

Question

Homework #4-Chapter13 (20pts for turned in on time) 1. (10pts) Binomial I distribution is a very important and common distribution in statistics, A binomial variable X is always COUNT of something. But not all count variables have binomial distributions. There are 4 binomial settings to justify whether a wariable X is a Binomial variable or not. a. There are a fixed number n of observations. b. The n observations are all independent. c. Each observation falls into just two categories. We define one of them as Success', and the other Failure d. The probability of success for a single observation (p) is the same for each observation Keep these in mind, and tell whether the variable X is a binomial variable or not. It has to satisfy all 4 settings to be binomial variable. If X is not a binomial variable, which of the setting did it not meet? (1) (25ptsMesearch shows that around 90% of the chicken eggs will hatch at 100-EX is the number of hatched eggs from an incubator set as 100 "F in a farm. (2) (2.5pts)Research shows that around 90% of the chicken eggs will hatch at 100 "F, but only 80% at 95 "F. In a farm, there are two incubators, and each have 20 eggs to hatch. One incubator is set at 100 "F and the other is set at 95-FX is the total number of hatched eggs from both incubators. (3) (25pts)Research shows that chicken eggs and duck eggs hatch rate at 100"F are both 90%, 10 chicken eggs and 10 duck eggs are put in an incubator controlled at 100·FX is the number of hatched eggs from the incubator (4) (25pts)When an opinion poll calls residential telephone numbers at random, only 20% of the phone calls reach a live person. X is the number of calls that reach a live person out of 20 dialings from the random digit dialing machine.

Explanation / Answer

a) Not a binomial variable since fixed number of observations are not known.

b)It is a not a binomial variable , butcan be expressed as a sum of binomial vriables. Observations are not independent.

c)Probability of success should be same. Not a binomial variable

d) C is not satisfied as there can be numbers which do not exist.

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