1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
timofeeve [1]
3 years ago
5

In the Ardmore Hotel, 20 percent of the guests (the historical percentage) pay by American Express credit card. (a) What is the

expected number of guests until the next one pays by American Express credit card? Expected number of guests (b) What is the probability that the first guest to use an American Express is within the first 10 to checkout? (Round your answer to 4 decimal places.) Probability
Mathematics
1 answer:
xxMikexx [17]3 years ago
3 0

Answer:

(a) The expected number of guests until the next one pays by American Express credit card is 4.

(b) The probability that the first guest to use an American Express is within the first 10 to checkout is 0.0215.

Step-by-step explanation:

The random variable <em>X</em> can be defined as the number of guests until the next one pays by American Express credit card

The probability that a guest paying by American Express credit card is, <em>p</em> = 0.20.

The random variable <em>X</em> follows a Geometric distribution since it is defined as the number of trials before the first success.

The probability mass function of <em>X</em> is:

P(X=x)=(1-p)^{x}p;\ x=0,1,2,3...,\ 0

(a)

The expected value of a Geometric distribution is:

E(X)=\frac{1-p}{p}

Compute the expected number of guests until the next one pays by American Express credit card as follows:

E(X)=\frac{1-p}{p}

         =\frac{1-0.20}{0.20}

         =4

Thus, the expected number of guests until the next one pays by American Express credit card is 4.

(b)

Compute the probability that the first guest to use an American Express is within the first 10 to checkout as follows:

P(X=10)=(1-0.20)^{10}\times0.20

                 =0.1073741824\times 0.20\\=0.02147483648\\\approx0.0215

Thus, the probability that the first guest to use an American Express is within the first 10 to checkout is 0.0215.

You might be interested in
The area of a parallelogram is 125 square inches and the height of the parallelogram is 10 inches. What is the lenght of the bas
Tasya [4]
12.5 inches is the answer
5 0
3 years ago
Read 2 more answers
In one day, 18 people each withdrew $100 from an atm machine.What was the overall change in the amount of money in the atm machi
tamaranim1 [39]

Answer:

1,800??

Step-by-step explanation:


7 0
3 years ago
Mr. Adamak earns a gross salary of $72,425. He
Mnenie [13.5K]

Answer:

$4345.5

Step-by-step explanation:

Income tax is 6% of total income. His income is $72425 so 6% (0.06) of $72425 is

$72425* 0.06= $4345.5

8 0
3 years ago
Can someone help me pls!!!
Cerrena [4.2K]

Answer:

First one: Function

Second one: not a function (a function cannot have two outputs)

Third one: Function

Last one: Not a function (doesn't pass vertical line test)

Step-by-step explanation:

Hope it helps!

6 0
3 years ago
Read 2 more answers
What isvequivalent to y=23x−6?
RUDIKE [14]

Answer:

Slope = 46.000/2.000 = 23.000

x-intercept = 6/23 = 0.26087

y-intercept = -6/1 = -6.00000

3 0
3 years ago
Other questions:
  • Find a negative real number such that the square of the sum of the number and 5 is equal to 48
    10·1 answer
  • Find the area of the figure <br> A)75in^2<br> B)70in^2<br> C)65in^2<br> D)80in^2
    10·1 answer
  • How do u guys solve this problem
    12·2 answers
  • Prove the the triangle with vertices a(−2,4,0), b(1,2,−1) and c(−1,1,2) is regular.
    12·1 answer
  • Please help me with these 2 answers!
    14·2 answers
  • Determine the quadrant (0.5)​
    10·1 answer
  • Branliest and Extra Points will be given!!! No explanation needed just the answer plz.
    14·1 answer
  • Christopher Columbus set sail from Spain in 1492. What year did the civil war end
    12·1 answer
  • A function is shown in the table below. If included in the table, which ordered pair would result in a relation that is no longe
    6·1 answer
  • What is the solution for x in the equation?<br> MIT<br> + ³ =<br> = 25<br> -<br> 25
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!