Question

In each situation, is it reasonable to use a binomial distribution for the random variable X? If the situation is not reasonable for a binomial distribution, select the correct statement that explains why.

(a) An auto manufacturer chooses one car from each hour's production for a detailed quality inspection. One variable recorded is the count X of finish defects (dimples, ripples, etc.) in the car's paint. Is it reasonable to use a binomial distribution for the random variable X? Select an answer choice.

A binomial distribution is not reasonable because there are more than two outcomes of interest.

A binomial distribution is not reasonable because ?p is not constant.

A binomial distribution is not reasonable because ?n is not fixed.

Yes, a binomial distribution is reasonable.

A binomial distribution is not reasonable because trials are not independent.

(b) The pool of potential jurors for a murder case contains 100 people chosen at random from the adult residents of a large city. Each person in the pool is asked in private whether he or she opposes the death penalty; X is the number who say "Yes." Is it reasonable to use a binomial distribution for the random variable X? Select an answer choice.

A binomial distribution is not reasonable because ?p is not constant.

A binomial distribution is not reasonable because there are more than two outcomes of interest.

A binomial distribution is not reasonable because trials are not independent.

A binomial distribution is not reasonable because ?n is not fixed.

Yes, a binomial distribution is reasonable.

(c) Joe buys a ticket in his state's Pick 3 lottery game every week; X is the number of times in a year that he wins a prize. Is it reasonable to use a binomial distribution for the random variable ?? Select an answer choice.

Yes, a binomial distribution is reasonable.

A binomial distribution is not reasonable because trials are not independent.

A binomial distribution is not reasonable because n is not fixed.

A binomial distribution is not reasonable because p is not constant.

A binomial distribution is not reasonable because there are more than two outcomes of interest.

Answer #1

Ans:

(a)**A binomial distribution is not reasonable because n
is not fixed**.

(b) **Yes, a binomial distribution is
reasonable.**

A binomial distribution is reasonable here; a “large city” will have a population much larger than 100 (the sample size), and each randomly selected juror has the same (unknown) probability p of opposing the death penalty.

n=100 and p=0.5

(c**)Yes, a binomial distribution is
reasonable.**

In a Pick 3 game, Joe’s chance of winning the lottery is the same every week, so assuming that a year consists of 52 weeks (n=52 ), this will have binomial distribution.

In each of the following situations, is it reasonable to use a
binomial distribution for the random variable XX? Give reasons for
your answer in each case.
(a) A manufacturer of medical catheters randomly selects eight
catheters, one from each hour's production for a detailed quality
inspection. One variable recorded is the count XX of catheters with
an unacceptable diameter (too small or too large).
A binomial distribution is reasonable. There is a fixed number
of catheters produced each day,...

Determine if the random variable from the experiment follows a
Binomial Distribution.
A random sample of 5 SLCC professors is obtained, and the
individuals selected are asked to state the number of years they
have been teaching at SLCC.
1. There there are two mutually exclusive outcomes
(success/failure).
[ Select ]
["FALSE",
"TRUE"]
2. Since a sample size of 5 is less than...

Suppose we have a binomial distribution with n trials
and probability of success p. The random variable
r is the number of successes in the n trials, and
the random variable representing the proportion of successes is
p̂ = r/n.
(a) n = 44; p = 0.53; Compute P(0.30
≤ p̂ ≤ 0.45). (Round your answer to four decimal
places.)
(b) n = 36; p = 0.29; Compute the probability
that p̂ will exceed 0.35. (Round your answer to four...

Let X be a binomial random variable with n =
400 trials and probability of success p = 0.01. Then the
probability distribution of X can be approximated by
Select one:
a. a Hypergeometric distribution with N =
8000, n = 400, M = 4.
b. a Poisson distribution with mean 4.
c. an exponential distribution with mean 4.
d. another binomial distribution with n =
800, p = 0.02
e.
a normal distribution with men 40 and variance 3.96.

Assume the random variable X has a binomial distribution with
the given probability of obtaining a success. Find the following
probability, given the number of trials and the probability of
obtaining a success. Round your answer to four decimal places.
P(X>3) P ( X > 3 ) , n=7 n = 7 , p=0.5 p = 0.5

Assume the random variable X has a binomial distribution with
the given probability of obtaining a success. Find the following
probability, given the number of trials and the probability of
obtaining a success. Round your answer to four decimal places.
P(X≥10) P ( X ≥ 10 ) , n=14 , p=0.8

Assume the random variable X has a binomial distribution with
the given probability of obtaining a success. Find the following
probability, given the number of trials and the probability of
obtaining a success. Round your answer to four decimal places.
P(X>3)P(X>3), n=5, p=0.8

Assume the random variable X has a binomial distribution with
the given probability of obtaining a success. Find the following
probability, given the number of trials and the probability of
obtaining a success. Round your answer to four decimal places.
P(X≤4), n=6, p=0.8

Assume the random variable X has a binomial distribution with
the given probability of obtaining a success. Find the following
probability, given the number of trials and the probability of
obtaining a success. Round your answer to four decimal places.
P(X≥16), n=19, p=0.7

Assume the random variable X has a binomial distribution with
the given probability of obtaining a success. Find the following
probability, given the number of trials and the probability of
obtaining a success. Round your answer to four decimal places.
P(X≥7), n=10, p=0.5

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