33. The population of Canada, y (in millions), can be approximated by the relation y=

AHarris Interactive survey for InterContinental Hotels & Resorts asked respondents, "When traveling internationally, do you

Sauron [17]

Answer:

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.

So

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

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

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.

3 0

4 years ago

Write a coordinate rule for the translation of f(x) to g(x).

Reil [10]

(x, y) → (x, y + n) - translate the graph n units up

(x, y) → (x, y - n) - translate the graph n units down

(x, y) → (x - n, y) - translate the graph n units left

(x, y) → (x + n, y) - translate the graph n units right

---------------------------------------------------------------------------

Look at the picture.

(x, y) → (x - 5; y + 4)

4 0

3 years ago

the distance light travels in one second (one light-second) is about 1.86 x 10^5 miles. Saturn is about 475 light-seconds from t

iris [78.8K]

The distance light travels in one second (one light second ) - 1.86 x 10^5 miles
Saturn is 475 light seconds away from the sun. Using this information we are asked to find the distance saturn is away from the sun.
1 light second - 1.86 x 10^5 miles
Therefore 475 light seconds -1.86 x 10^5 miles/light second * 475 light seconds
= 8.83 x 10^7 miles
Saturn is 8.83 x 10^7 miles away from the sun

7 0

4 years ago

Read 2 more answers

Sarah and her 4 Friends share some cookies. If each person gets 3 cookies, how many cookies were shared? Write a mathematical eq

Alexeev081 [22]

Answer:

The answer is the 2nd one im pretty sure

Step-by-step explanation:

4 0

3 years ago

The _____ is the price of an item that is being offered at a lower price than usual.

Svetlanka [38]

Answer:

sale price

Step-by-step explanation:

price of an item that is being offered at a lower price than usual

8 0

2 years ago