Mathematics, 16.10.2019 22:30 keilahkimbrough8

Aharris interactive survey for intercontinental hotels & resorts asked respondents, "when traveling internationally, do you generally venture out on your own to experience culture, or stick with your tour group and itineraries? " the survey found that 23% of the respondents stick with their tour group (usa today, january 21, 2004). a. in a sample of six international travelers, what is the probability that two will stick with their tour group? b. in a sample of six international travelers, what is the probability that at least two will stick with their tour group? c. in a sample of 10 international travelers, what is the probability that none will stick with the tour group?

Answers: 2

Show answers

Answers

Answer from: Mrdwarf7163

a) There is a 27.89% probability that two will stick with their tour group.

b) There is a 41.81% that in at least two will stick with their tour group.

c) There is a 7.33% probability that none will stick with their tour group.

Step-by-step explanation:

For each responders, this question can only have two outcomes. Either they stick with their tour group, or they don't. So this means that we can solve this problem as binomial distribution.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

In which $C_{n,x}$ is the number of different combinatios of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And $\pi$ is the probability of X happening.

For these problems

The survey found that 23% of the respondents stick with their tour group, so $\pi = 0.23$ .

a. In a sample of six international travelers, what is the probability that two will stick with their tour group?

The sample has six travelers, so n = 6 .

We want P(X = 2).

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

$P(X = 2) = C_{6,2}.(0.23)^{2}.(0.77)^{4} = 0.2789$

There is a 27.89% probability that two will stick with their tour group.

b. In a sample of six international travelers, what is the probability that at least two will stick with their tour group?

Either less than two stick with their groups, or at least two do. The sum of these probabilities is decimal 1.

$P(X < 2) + P(X \geq 2) = 1$

$P(X \geq 2) = 1 - P(X < 2)$

In which

P(X < 2) = P(X = 0) + P(X = 1)

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

$P(X = 0) = C_{6,0}.(0.23)^{0}.(0.77)^{6} = 0.2084$

$P(X = 1) = C_{6,1}.(0.23)^{1}.(0.77)^{5} = 0.3735$

-----

P(X < 2) = P(X = 0) + P(X = 1) = 0.2084 + 0.3735 = 0.5819

$P(X \geq 2) = 1 - P(X < 2) = 1 - 0.5819 = 0.4181$

There is a 41.81% that in at least two will stick with their tour group.

c. In a sample of 10 international travelers, what is the probability that none will stick with the tour group?

Now our sample has 10 travelers, so n = 10 .

We want to find P(X = 0)

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

$P(X = 0) = C_{10,0}.(0.23)^{0}.(0.77)^{10} = 0.0733$

There is a 7.33% probability that none will stick with their tour group.

Answer from: Quest

vbbv

step-by-step explanation:

Answer from: Quest

grab rope, tie a loop-de-loop, put it around ur neck, now jump while its tied to a high place. now your shoes are cool.

step-by-step explanation:

Another question on Mathematics

Mathematics, 21.06.2019 18:00

Marla bought a book for $12.95, a binder for $3.49, and a backpack for $44.99. the sales tax rate is 6%. find the amount of tax and the total she paid for these items

Answers: 3

Answer

Mathematics, 21.06.2019 22:10

Erinn wrote the equation –5x + 4y = 32 to represent her hourly wage (y) and how this wage has changed during each year that she worked at a company (x). what is the rate of change in erinn's hourly wage per year?

Answers: 2

Answer

Mathematics, 22.06.2019 00:00

Plz answer asap! i will reward brainliest and 12 points for these three questions!take notice: these three questions are completely different! 1) what is the percentage of sugar in the syrup made of 10 kg of water and 4 kg of suugar? 2) what was the original price if after 10% discount it became $450? 3) at first a price was decreased by 12%, then it was disounted again by an additional 5%. what is the percent of the total discount? , and remeber i will award brainliest and 12 points!

Answers: 1

Answer

Mathematics, 22.06.2019 01:20

Graph the following system of linear inequalities. identify at least two points in the solution: y < 5 - 2x | x + 5y > -7

Answers: 2

Answer

You know the right answer?

Aharris interactive survey for intercontinental hotels & resorts asked respondents, "when trave...

Questions