Question

Ask Your Teacher NBC News reported on May 2, 2013, that 1 in 20 children in the United States have a food allergy of some sort. Consider selecting a random sample of 15 children and let X be the number in the sample who have a food allergy. Then X ~ Bin(15, 0.05). (Round your probabilities to three decimal places.)

(a) Determine both P(X ≤ 2) and P(X < 2). P(X ≤ 2) = P(X < 2) =

(b) Determine P(X ≥ 3). P(X ≥ 3) =

(c) Determine P(1 ≤ X ≤ 2). P(1 ≤ X ≤ 2) =

(d) What are E(X) and σX? (Round your answers to two decimal places.) E(X) = σX =

(e) In a sample of 30 children, what is the probability that none has a food allergy?

Answer #1

A news company reported that 8% of adult Americans have a food
allergy. Consider selecting 15 adult Americans at random. Define
the random variable x as x = number of people in the sample of 15
that have a food allergy. Find the following probabilities. (Round
your answers to three decimal places.)
(a)P(x < 2)
(b)P(x ≤ 2)
(c)P(x ≥ 3)
(d)P(1 ≤ x ≤ 2)

ASK YOUR TEACHER
You may need to use the appropriate technology to answer this
question.
Use the sample data below to test the hypotheses
H0:
p1 = p2 =
p3
Ha:
not all
population proportions are equal
where
pi
is the population proportion of Yes responses for population
i.
Response
Populations
1
2
3
Yes
145
145
106
No
95
145
114
Find the value of the test statistic. (Round your answer to
three decimal places.)
Find the p-value. (Round...

When circuit boards used in the manufacture of compact disc
players are tested, the long-run percentage of defectives is 10%.
Let X = the number of defective boards in a random sample
of size n = 20, so X ~ Bin(20, 0.1). (Round your
probabilities to three decimal places.)
(a) Determine P(X ≤ 2).
(b) Determine P(X ≥ 5).
(c) Determine P(1 ≤ X ≤ 4).
(d) What is the probability that none of the 20 boards is
defective?
(e)...

When circuit boards used in the manufacture of compact disc
players are tested, the long-run percentage of defectives is 10%.
Let X = the number of defective boards in a random sample
of size n = 20, so X ~ Bin(20, 0.1). (Round your
probabilities to three decimal places.)
(a) Determine P(X ≤ 2).
(b) Determine P(X ≥ 5).
(c) Determine P(1 ≤ X ≤ 4).
(d) What is the probability that none of the 20 boards is
defective?
(e)...

Suppose that x is a binomial random variable with
n = 5, p = .56, and q = .44.
(b) For each value of x, calculate
p(x). (Round final
answers to 4 decimal places.)
p(0) =0.0164
p(1) =0.1049
p(2) =0.2671
p(3) =0.3399
p(4) =0.2163
p(5) =0.0550
(c) Find P(x = 3).
(Round final answer to 4 decimal
places.)
P(x = 3)
0.3399selected answer
correct
(d) Find P(x ≤ 3).
(Do not round intermediate calculations.
Round final answer to 4 decimal...

1. Compute the mean and variance of the following probability
distribution. (Round your answers to 2 decimal
places.)
x
P(x)
4
0.10
7
0.25
10
0.30
13
0.35
2. Given a binomial distribution with n = 6 and π=
.25. Determine the probabilities of the following events using the
binomial formula. (Round your answers to 4 decimal
places.)
x = 2
x = 3
3. A probability distribution is a listing of all the outcomes
of an experiment and the...

ASK YOUR TEACHER
question
Bill Alther is a zoologist who studies Anna's hummingbird
(Calypte anna). (Reference: Hummingbirds, K. Long, W.
Alther.) Suppose that in a remote part of the Grand Canyon, a
random sample of six of these birds was caught, weighed, and
released. The weights (in grams) were as follows.
3.7
2.9
3.8
4.2
4.8
3.1
The sample mean is = 3.75 grams. Let x be a
random variable representing weights of hummingbirds in this part
of the Grand Canyon....

Consider the probability distribution shown below.
x
0
1
2
P(x)
0.05
0.50
0.45
Compute the expected value of the distribution.
Consider a binomial experiment with
n = 7 trials
where the probability of success on a single trial is
p = 0.10.
(Round your answers to three decimal places.)
(a) Find
P(r = 0).
(b) Find
P(r ≥ 1)
by using the complement rule.
Compute the standard deviation of the distribution. (Round your
answer to four decimal places.)
A...

1. A poll of 2234 U.S. adults found that 31% regularly used
Facebook as a news source.
Find the margin of error and confidence interval for the
percentage of U.S. adults who regularly use Facebook as a news
source, at the 90% level of confidence. Round
all answers to 2 decimal places.
Margin of Error (as a percentage):
Confidence Interval: % to %
Find the margin of error and confidence interval for the
percentage of U.S. adults who regularly use...

Question 1)
Tay-Sachs disease is a genetic disorder that is usually fatal in
young children. If both parents are carriers of the disease, the
probability that each of their offspring will develop the disease
is approximately 0.25. Suppose a husband and wife are both carriers
of the disease and the wife is pregnant on three different
occasions. If the occurrence of Tay-Sachs in any one offspring is
independent of the occurrence in any other, what are the
probabilities of these...

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