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
bogdanovich [222]
2 years ago
9

An airplane has 100 seats for passengers. Assume that the probability that a person holding a ticket appears for the flight is 0

.90. If the airline sells 105 tickets, what is the probability that everyone who appears for the flight will get a seat
Mathematics
1 answer:
zmey [24]2 years ago
7 0

Answer:

96.33% probability that everyone who appears for the flight will get a seat

Step-by-step explanation:

I am going to use the binomial approximation to the normal to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

\sqrt{V(X)} = \sqrt{np(1-p)}

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that \mu = E(X), \sigma = \sqrt{V(X)}.

In this problem, we have that:

n = 105, p = 0.9

So

\mu = E(X) = np = 105*0.9 = 94.5

\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{105*0.9*0.1} = 3.07

What is the probability that everyone who appears for the flight will get a seat

100 or less people appearing to the flight, which is the pvalue of Z when X = 100. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{100 - 94.5}{3.07}

Z = 1.79

Z = 1.79 has a pvalue of 0.9633

96.33% probability that everyone who appears for the flight will get a seat

You might be interested in
One cup of​ grated, fresh Parmesan cheese weighs 3 ounces. How many cups of grated cheese can you expect to get from a​ 4.5-poun
Ksenya-84 [330]

Answer:

9 cups

Step-by-step explanation:

If one pound is equal to 2 cups, then you would multiply 2 by 4, which gives you 8. If one pound equals 2 cups, then half a pound equals 1 cup. So since we already have 8 cups, you just add one more cup, which gives you 9 cups total

SUMMARY: You can expect to get 9 cups of grated parmesan cheese from a 4.5-pound block.

5 0
2 years ago
3+6X2^3/3<br><br>Please explane me well 2^3 how can i do
victus00 [196]
Your answer would be 19
4 0
2 years ago
The value of a car is deprecting at the rate of 12% Find the correct value of car when cost of car was rs 350000
kow [346]

Answer:

The cost of the car is $ RS 308,000.

Step-by-step explanation:

Given that the value of a car is deprecting at the rate of 12%, to find the correct value of car when cost of car was $ RS350,000 last year, the following mathematical calculation must be performed:

100 - 12 = 88

88/100 = 0.88

350,000 x 0.88 = X

308,000 = X

Therefore, the cost of the car is $ RS 308,000.

8 0
3 years ago
Ms. Smith and Mr. Roberts are running a race. Ms. Smith runs 8, 305 feet. Mr. Roberts runs 2 miles. How many feet further does M
Tcecarenko [31]

Answer:

Mr. Roberts runs 2,255 more feet then Ms. Smith.

Step-by-step explanation:

So I took 5,280 + 5,280 = 10,560 so now I can just take Ms. Smith's 8,305 and subtract it from 10,560 which gave me 2,255 so Mr. Roberts runs 2,255 more feet then Ms. Smith.

3 0
3 years ago
3/13 as a decmal ronded to the nearest hundeth
Illusion [34]
Simple...

you have: \frac{3}{13}

Dividing-->>

0.23076923

But, remember, you're rounding to the nearest hundreth...

0.23

Thus, your answer.
8 0
3 years ago
Other questions:
  • To the nearest thousand , the population of Texas was estimated to be 24,327,000 in 2008 . describe the actual population that T
    5·2 answers
  • Mercedes bought 2 1/2 pounds of blueberries and her son ate 1/4 the blueberries how many pounds of blueberries Are left?
    8·1 answer
  • Mary has 1/4 of a tank of gas.A quarter or a tank is equal to 5 gallons how many gallons does her tank hold
    7·1 answer
  • What are the zeros of the polynomial function?
    12·2 answers
  • Two children of a sandwich.How much will each child get
    15·1 answer
  • Insert three arithmetic means between 4 and 10.
    5·1 answer
  • (please help) look at the picture below
    6·1 answer
  • For a right triangle ABC, you are told that cos A = x and sin A = y. Which option below gives an expression that is equivalent t
    9·1 answer
  • Find the x-intercepts for the parabola defined
    9·1 answer
  • This month is October.Which month will 2451 months later be.
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!