answer.
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
lana [24]
1 year ago
8

An airline makes 200 reservations for a flight who holds 185 passengers. The probability that a passenger arrives for the flight

is 0.9 and the passengers are assumed to be independent. Use the normal approximation of Binomial distribution to answer the following questions.
a. Approximate the probability that all the passengers who arrives can be seated.
b. Approximate the probability that there are empty seats.
c. Approximate the number of reservations that the airline should make so that the probability that everyone who arrives can be seated is 0.95.
Mathematics
1 answer:
SVEN [57.7K]1 year ago
3 0

Answer:

The answer is below

Step-by-step explanation:

given that:

n = sample size = 200, p = probability of a cancelled reservation = 1 - 0.9 = 0.1

The z score is given by:

z=\frac{x-mean}{standard\ deviation} =\frac{x-np}{\sqrt{np(1-p)} }

a) The probability that all the passengers who arrives can be seated can only occur if atleast 15 or more passengers cancelled their reservations.

P(X ≥ 15) = 1 - P(X ≤ 14.5)

z=\frac{x-np}{\sqrt{np(1-p)} }=\frac{14.5-(200*0.1)}{\sqrt{(200*0.1)(1-0.1)} }=-1.3

From the normal distribution table:

P(X ≥ 15) = 1 - P(X ≤ 14.5) = 1 - P(z < -1.3) = 1 - 0.0968 = 0.9

b) The probability that there are empty seat only occur if atleast 16 or more passengers cancelled their reservations.

P(X ≥ 16) = 1 - P(X ≤ 15.5)

z=\frac{x-np}{\sqrt{np(1-p)} }=\frac{15.5-(200*0.1)}{\sqrt{(200*0.1)(1-0.1)} }=-1.06

From the normal distribution table:

P(X ≥ 16) = 1 - P(X ≤ 15.5) = 1 - P(z < -1.06) = 1 - 0.1446 = 0.8554

c)

0.95=P(X\geq n-185)=1-P(X\leq n-185)\\\\P(X\leq n-185)=1-0.95\\\\P(X\leq n-185)=0.05\\\\0.05=P(Z

You might be interested in
How would the fraction 1/3+square root of 2 be rewritten if its denominator is rationalized using difference of squares? A. 3-sq
Vera_Pavlovna [14]

C

given 1 /( 3 + √2 )

then rationalise the denominator by multiplying the numerator/ denominator by the conjugate of the denominator

the conjugate of 3 + √2 is 3 - √2

1 / (3 + √2 ) × (3 - √2 ) / (3 - √2 )

= (3 - √2 ) /( 9 - 2 ) = (3 - √2 ) / 7

4 0
1 year ago
Read 2 more answers
Of 560 samples of seafood purchased from various kinds of food stores in different regions of a country and genetically compared
frutty [35]

Answer:

a) (0.5256,0.5944)  

c) Criticism is invalid

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 560

Proportion of mislabeled = 56%

\hat{p} = 0.56

a) 90% Confidence interval:

\hat{p}\pm z_{stat}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}

z_{critical}\text{ at}~\alpha_{0.05} = \pm 1.64

Putting the values, we get:

0.56\pm 1.64(\sqrt{\dfrac{0.56(1-0.56)}{560}}) = 0.56\pm 0.0344\\\\=(0.5256,0.5944)

b) Interpretation of confidence interval:

We are 90% confident that the true proportion of all seafood in the country that is mislabeled or misidentified is between 0.5256 and 0.5944 that is 52.56% and 59.44%.

c) Validity of criticism

Conditions for validity:

np > 10\\n(1-p)>10

Verification:

560\times 0.56 = 313.6>10\\560(1-0.56) = 246.4>10

Both the conditions are satisfied. This, the criticism is invalid.

8 0
2 years ago
What ratio is equivalent to the ratio 18:24
Lana71 [14]

Answer:

3/4

Step-by-step explanation:

18:24=18/24

18/24 reduces to 3/4

3 0
2 years ago
The radius of a cylindrical construction pipe is 1.5ft . If the pipe is 14ft long, what is its volume? Use the value 3.14 for π
Lady bird [3.3K]

Answer:

Volume of cylinder =989 ft cube

Step-by-step explanation:

<u>Volume of cylinder</u>

Volume V = πr²h

r - radius and h - height

It is given that,

The radius of a cylindrical construction pipe is 1.5ft and

Length of pipe = 14 ft

<u>To find volume of cylinder</u>

Volume V = πr²h

V = 3.14 x 1.5 x1.5 x 14 =989.1 ≈ 989 ft cube

5 0
1 year ago
A building has eight levels above ground and one level below ground. The height of each level from floor to ceiling is 14 1/2 fe
vovangra [49]
The net change in elevation is 72.5 feet
6 0
1 year ago
Read 2 more answers
Other questions:
  • The two-way frequency table shows the results of a survey of a certain forest. Find the probability that a randomly chosen tree
    13·2 answers
  • Given the circle with the equation (x - 3)2 + y2 = 49, determine the location of each point with respect to the graph of the cir
    9·2 answers
  • Suppose the graph of a cubic polynomial function has the same zeroes and passes through the coordinate (0, –5). Describe the ste
    11·2 answers
  • 1. Let’s assume the following statements are true: Historically, 75% of the five­star football recruits in the nation go to univ
    9·1 answer
  • A chemist needs 30mL of a 12% acid solution for an experiment. The lab has available a 10% solution and a 25% solution. How many
    13·1 answer
  • 67,124 x three fourths = ________. Will the product of this equation be less than or greater than 67,124? Explain your reasoning
    9·2 answers
  • Over the weekend Pop's Pizza Shack sold 53 pepperoni, 43 sausage, 61 cheese, 42 mushroom, 48 hamburger and 41 combination pizzas
    8·2 answers
  • For what values (cases) of the variables the expression does not exist: a/2x−4 (That equation is a fraction)
    13·1 answer
  • Repeated-measures and matched-subjects experiments Aa Aa Repeated-measures experiments measure the same set of research particip
    11·1 answer
  • The solution to that equation is p=500. What does the solution mean?
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!