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Varvara68 [4.7K]
1 year ago
14

A small regional carrier accepted 23 reservations for a particular flight with 19 seats. 18 reservations went to regular custome

rs who will arrive for the flight. Each of the remaining passengers will arrive for the flight with a 50% chance, independently of each other.(Report answers accurate to 4 decimal places.)Find the probability that overbooking occurs. Find the probability that the flight has empty seats.
Mathematics
1 answer:
madreJ [45]1 year ago
8 0

We remove the 18 regular customers and their seats from consideration.

Thus, we consider the 23 - 18 remaining customers = 5; and 19 - 18 = 1 seat.

Overbooking means 3 or more of the 5 remaining passengers; each has a 50% chance remaining.

Overbooking = 1 - P(X ≤ 2) = 0.5

Probability of empty seats = P(X ≤ 1) = 0.1875

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the length of a rectangle is 2 inches less than 3 times it width . The perimeter of the rectangle is 124 inch. WHat is the lengt
vitfil [10]

Step-by-step explanation:

let w = width

length = 3w-2

perimeter = 2*length + 2*width

perimeter = 2(3w-2) + 2w

perimeter = 6w - 4 + 2w

perimeter = 8w - 4

perimeter = 124 inch

8w - 4 = 124inch

<em>+4 to each side</em>

8w = 128inch

<em>divide each side by 8</em>

w = 16

length = 3w-2

           = 3(16) - 2

length = 46 inch

5 0
3 years ago
Tom opens a bank account and makes an initial deposit of 500$. Then banker tells Tom that he is going to receive an annual rate
Arturiano [62]

~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$500\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &15 \end{cases} \\\\\\ A=500\left(1+\frac{0.06}{1}\right)^{1\cdot 15}\implies A=500(1.06)^{15}\implies A\approx 1198.28

5 0
2 years ago
Let g(x)= -x^2+4x+4. Find g(p). g(p)=_____
mixer [17]

Answer:

g(p)= -p^2+4p+4

Step-by-step explanation:

g(x)= -x^2+4x+4

Replace x with p

g(p)= -p^2+4p+4

8 0
4 years ago
Suppose that 37% of college students own cats. If you were to ask random college students if they own a cat what would the proba
Likurg_2 [28]

Using the binomial distribution, the probabilities are given as follows:

a) 0.37 = 37%.

b) 0.5065 = 50.65%.

c) 0.3260 = 32.60%.

<h3>What is the binomial distribution formula?</h3>

The formula is:

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

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

The parameters are:

  • x is the number of successes.
  • n is the number of trials.
  • p is the probability of a success on a single trial.

For this problem, the fixed parameter is:

p = 0.37.

Item a:

The probability is P(X = 1) when n = 1, hence:

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 1) = C_{1,1}.(0.37)^{1}.(0.63)^{0} = 0.37

Item b:

The probability is P(X = 3) when n = 3, hence:

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 3) = C_{3,3}.(0.37)^{3}.(0.63)^{0} = 0.5065

Item c:

The probability is P(X = 2) when n = 4, hence:

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 2) = C_{4,2}.(0.37)^{2}.(0.63)^{2} = 0.3260

More can be learned about the binomial distribution at brainly.com/question/24863377

#SPJ1

4 0
2 years ago
86,921 in expanded form
Rudik [331]
86921 = 80000 + 6000 + 900 +20 +1
3 0
3 years ago
Read 2 more answers
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