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
horrorfan [7]
3 years ago
6

An airline finds that 5% of the persons making reservations on a certain flight will not show up for the flight. If the airline

sells 105 tickets for a flight that has only 100 seats, what is the probability that a seat will be available for every person holding a reservation and planning to fly? (Round your answer to four decimal place
Mathematics
1 answer:
vivado [14]3 years ago
6 0

Answer:

The answer to the question is;

The probability that a seat will be available for every person holding a reservation and planning to fly is 0.63307.

Step-by-step explanation:

Let the sample size =n = 100

The success probability = 5 % = 0.05

Number of tickets sold = 105 tickets

In the case where there the airline has found that 5 % will not show up, then every passenger should have  a seat, we have  

A Binomial distribution is appropriate where there is a chance for a certain number of successful outcomes from a number of independent trails

However n·p and n·q must be ≥ 5 for there to be a normal approximation of a Binomial distribution thus

n·p = 105×0.05 =  5.25 ≥ 5

and n·q = n(1 - p) = 105 (1 - 0.05) = 99.75 ≥ 5

As the requirements are met, we can proceed with the approximation of the Binomial distribution by the normal distribution

 z = \frac{x-np}{\sqrt{np(1-p)}  } = \frac{4.5 - 105*0.05}{\sqrt{105*0.05(1-0.05)} } =  - 0.3358

We therefore have P(x ≥ 5) = P( x > 4.5) = P(z > -0.34) = 1 - P(z < -0.34) = 1 -0.36693 = 0.63307

Another way to solve the question is as follows

p = 0.95 q = 0.05

μ = np = 0.95*105 = 99.75, σ = \sqrt{npq} = 2.233

P (x≤100) = P(z = P(z<0.34) = 0.63307.

You might be interested in
Bradbury scar caught 35 fish with his net 20 percent of the fish had to be thrown back into the sea because they were too small
Lerok [7]
7 fish were thrown back
6 0
2 years ago
The net of a cylinder is shown. The area of one base of the cylinder is 9Pi in.2. The circumference of a base is 6Pi in., and th
hram777 [196]

Answer:

9Pi + 9Pi + 6Pi(10) in.^2

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
If​ f(x) is continuous on a closed​ interval, then it is enough to look at the points where f prime (x )equals0 in order to find
aivan3 [116]
This would be false
5 0
3 years ago
How many quarters are in $375.75?​
DanielleElmas [232]

Answer:

1503 quarters

Step-by-step explanation:

There are 4 quarters in 1 dollar, so we multiply this number by 4.

375.75 * 4 = 1503

7 0
2 years ago
Read 2 more answers
Solve for b. Help! Explain steps!
Doss [256]

Answer:

what is the unit and class

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
Other questions:
  • The product of a number and -7 gives seven times the sum of that number and -40. Find the number
    8·1 answer
  • 3/2 times 2/3 in the simplest form
    14·1 answer
  • Plssss helpppp ASAPP<br> will mark BRAINLIEST!!!
    13·2 answers
  • The diameter of a circle is 14 m. Find its area to the nearest tenth.
    7·1 answer
  • Two students were asked to find the value of a $1000 item after 3 years. The item was depreciating (losing value) at a rate of 4
    14·1 answer
  • Lin is running on a track. Lin runs 5 laps around a track in 6 minutes. How many laps per minute is that? (Round to the nearest
    11·2 answers
  • The measures of the angles of a triangle are shown in the figure below. Solve for x.
    5·1 answer
  • What is the slope of the tine that passes through the points (1/4,3) and (5,8)?
    12·1 answer
  • Anyone happen to know this?
    9·1 answer
  • Use the figure to answer the question.<br> What is the area of the triangle on the left?
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!