Use the geometric probability distribution to solve the following problem. On the leeward side of the island of Oahu, in a small village, about 74% of the residents are of Hawaiian ancestry. Let n = 1, 2, 3, … represent the number of people you must meet until you encounter the first person of Hawaiian ancestry in the village. (a) Write out a formula for the probability distribution of the random variable n. (Enter a mathematical expression.) P(n) = p(1 - p)n-1 (b) Compute the probabilities that n = 1, n = 2, and n = 3. (For each answer, enter a number. Round your answers to three decimal places.) P(1) = 0.740 P(2) = 0.192 P(3) = 0.050 (c) Compute the probability that n ≥ 4. Hint: P(n ≥ 4) = 1 − P(n = 1) − P(n = 2) − P(n = 3). (Enter a number. Round your answer to three decimal places.) 0.018 (d) What is the expected number of residents in the village you must meet before you encounter the first person of Hawaiian ancestry? Hint: Use μ for the geometric distribution and round. (Enter a number. Round your answer to the nearest whole number.) residents

Answer:

(a) [tex]\text{P(n)} = \text{p} \times \text{(1 - p)}^{n-1} ; \text{ n} = 1, 2, 3,....[/tex]

(b) P(1) = 0.740, P(2) = 0.192, and P(3) = 0.050.

(c) The probability that n ≥ 4 is 0.018.

(d) The expected number of residents in the village you must meet before you encounter the first person of Hawaiian ancestry is 3.

Step-by-step explanation:

We are given that on the leeward side of the island of Oahu, in a small village, about 74% of the residents are of Hawaiian ancestry.

Let n = 1, 2, 3, … represent the number of people you must meet until you encounter the first person of Hawaiian ancestry in the village.

(a) We can observe that the above situation can be represented through the geometric distribution because the geometric distribution states that we will keep on going with the trials until we achieve our first success,

Here also, n represent the number of people you must meet until you encounter the first person of Hawaiian ancestry in the village.

So, the probability distribution of the geometric distribution is given by;

[tex]\text{P(n)} = \text{p} \times \text{(1 - p)}^{n-1} ; \text{ n} = 1, 2, 3,....[/tex]

where, p = probability that the residents are of Hawaiian ancestry = 74%

(b) The probabilities that n = 1, n = 2, and n = 3 is given by;

[tex]\text{P(n)} = \text{p} \times \text{(1 - p)}^{n-1}[/tex]

P(1) = [tex]\text{0.74} \times \text{(1 - 0.74)}^{1-1}[/tex] = 0.74

P(2) = [tex]\text{0.74} \times \text{(1 - 0.74)}^{2-1}[/tex] = 0.192

P(3) = [tex]\text{0.74} \times \text{(1 - 0.74)}^{3-1}[/tex] = 0.050

(c) The probability that n ≥ 4 is given by = P(n ≥ 4)

     P(n ≥ 4) = 1 - P(n = 1) - P(n = 2) - P(n = 3)

                   = 1 - 0.74 - 0.192 - 0.050

                   = 0.018

(d) The expected number of residents in the village you must meet before you encounter the first person of Hawaiian ancestry is given by = E(n)

We know that the mean of the geometric distribution is given by;

           Mean = [tex]\dfrac{p}{1-p}[/tex] = [tex]\dfrac{0.74}{1-0.74}[/tex]

                     = [tex]\dfrac{0.74}{0.26}[/tex] = 2.85 or 3 (approx).

If its -26 degree in Canada and 34 degrees in Australia what is the difference in temperature

1/2 of a number reduced by six times the same number algebraic expression

60 POINTS!!!


10. Which of the following tables represents a function where f(4) = 6 and f(−1) = −4 ?

A. x...
f of x...
zero... two....
four... six...
six... eight...
A.

B. x...
f of x...
negative one... negative four...
zero... zero...
two... eight...
B. , , ,

C. x...
f of x...
negative four... negative ten...
negative one... negative four...
six.... ten....
C. , ,

D.

Computisional Science

Write the rate as a unit rate. 4 inches of rain in 10 hours. (Inches per hour)

what is 5 to the power of 10

Which of the following is the correct factorization of the polynomial below 2X squared -16 X +32

what is the scale factor of the dilation

Plssssss answer thjs quet

Which is the correct answer?

help me please i’m stuck, thank you

Can someone help me plzzz

the difference of a number and 10 is at least 5 more than 9 times the number

Help me pls i give brainliest

Julio and Kyle hike along the same trail. Kyle hikes the first 6 miles in 2 hours. Who hikes more quickly?

Step 1: m2m+mZn +mzo = 180 degrees (sum of angles of a triangle)
Step 2: mp +mZo = 180 degrees (adjacent supplementary angles)
Step 3: Therefore, mZm+mZn+mZo=mZn + MZD Step 4: So.mZm+mZn=mZp
In which step did the student first make a mistake and how can i be corrected?
Step 1: it should be mZm+mZnam 2990 degrees (corresponding angles)
Step 1: I should be mm +mZn+mZo = 90 degrees (adjacent angles)
Step 3: t should be mZm+mZnm Zo=mZo-mZp Step 2. n should be mZo-mZo=90 degrees (complementary angles) -​

A recipe requires 3/4 of a cup of milk for every 1 1/2 cups of flour how many cups of milk are needed for each cup of flour

Is 45/60 equal to 75/100?

455 What is the minimum number of square marbles required to tile a floor of length 6 meter 24
cm. and width 4 meter 16 cm?
A. 6
B. 12
C. 14
D. 8​

IN THE CENTRAL CITY GRAND PRIX, OUT OF 50 CARS THAT STARTED THE RACE, 12
OF THEM FINISHED. WHAT PERCENT OF THE CARS FINISHED THE RACE? WHAT
PERCENT DID NOT FINISH THE RACE?
I need a step by step explanation please !!!

pls help me with this​

Company A charges a $100 annual fee plus a $9/hr car share fee. Company B
charges $120 plus $7/hr. What is the minimum number of hours that a car
share needs to be used per year to make Company B a better deal?
O A. 11
O B. 10
O C. 12
O D. 9

Find the slope of the line passing
through (2,5) and (-3, -6).

Let ​f(x)=x2−18 and ​g(x)=17−x. Perform the composition or operation indicated.
f/g​(−8​)

Juan is creating a rectangular garden in his backyard. The length of the garden is 20 feet. The perimeter of the garden must be at least 70 feet and no more than 86 feet. Use a compound inequality to find the range of values for the width w of the garden.

Four friends were making cards to sell at the holiday sale. Each friend made 9 cards. They put all their cards together and then bundled them in groups of 6 cards to sell. How many bundles of 6 cards did they make? Show all your work.

m
/
n
(x), x not equal to

what is the positive difference between 19&8?​

(a) Which of the following expresses the zero product property formally using quantifiers and variables? ∀ real numbers x and y, if xy = 0 then x = 0 and y = 0. ∀ real numbers x and y, if x = 0 and y = 0 then xy = 0. ∀ real numbers x and y, if x = 0 or y = 0 then xy = 0. ∀ real numbers x and y, if xy = 0 then x = 0 or y = 0. (b) Which of the following is the contrapositive of the zero product property? ∀ real numbers x and y, if x ≠ 0 or y ≠ 0 then xy ≠ 0. ∀ real numbers x and y, if xy ≠ 0 then x ≠ 0 or y ≠ 0. ∀ real numbers x and y, if x ≠ 0 and y ≠ 0 then xy ≠ 0. ∀ real numbers x and y, if xy ≠ 0 then x ≠ 0 and y ≠ 0. (c) Which of the following is an informal version (without quantifier symbols or variables) for the contrapositive of the zero product property? For any two real numbers, if at least one of them is nonzero then their product is nonzero. If the product of two real numbers is nonzero, then both numbers are nonzero. If the product of two real numbers is nonzero, then neither number is zero. If neither of two real numbers is zero, then their product is nonzero.

At a carnival, Ryan bought 7 packs of 14 tickets each. He has used 39 of the tickets so far.