For each scenario described below, 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.
For each scenario described below, 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 semiconductor 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. Reconsider the situation in part (f). Now, suppose the sample of 40 chips consists of
chips with 1 and with 0 defects.
h. A filling operation attempts to fill detergent packages to the advertised weight. Let X
denote the number of detergent packages that are underfilled.
i. 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.
j. Let X denote the number of surface flaws in a large coil of galvanized steel.
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
