Question

For each scenario (a)–(h), state whether or not the binomial distribution is a reasonable model for the random variable and why. State any assumptions you make.

a. A production process produces thousands of temperature transducers. Let X denote the number of nonconforming transducers in a sample of size 30 selected at random from the process.

b. From a batch of 50 temperature transducers, a sample of size 30 is selected without replacement. Let X denote the number of nonconforming transducers in the sample.

c. Four identical electronic components are wired to a controller that can switch from a failed component to one of the remaining spares. Let X denote the number of components that have failed after a specified period of operation.

d. Let X denote the number of accidents that occur along the federal highways in Arizona during a one-month period.

e. Let X denote the number of correct answers by a student taking a multiple-choice exam in which a student can eliminate some of the choices as being incorrect in some questions and all of the incorrect choices in other questions.

f. Defects occur randomly over the surface of a semicon- ductor chip. However, only 80% of defects can be found by testing. A sample of 40 chips with one defect each is tested. Let X denote the number of chips in which the test finds a defect.

g. Errors in a digital communication channel occur in bursts that affect several consecutive bits. Let X denote the number of bits in error in a transmission of 100,000 bits.

h. Let X denote the number of surface flaws in a large coil of galvanized steel.

Answer 1

A)

As we have sample of 30 and so must be there is an estimate of probability that any transducer is defective then we got both n=30 and P so yes it's binomial distribution.

b)

Since there are total 50 items and then we have selected 30 from that batch so if X is number of defective in 30 then we can say that X is hypergeometric distribution but not binomial.

c)

If P is probability of any component failure so we have 4 identical components and X is number of components out of 4 that have failed hence it's binomial.

d)

As we are finding the number of accidents on highway here we don't have any data regarding sample size or any Probability but we can estimate rate of incidents per month so it's Poisson distribution not binomial