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
Maslowich
3 years ago
12

One strange phenomenon that sometimes occurs at U.S. airport security gates is that an otherwise law-abiding passenger is caught

with a gun in his/her carry-on bag. Usually the passenger claims he/she forgot to remove the handgun from a rarely-used bag before packing it for airline travel. It’s estimated that every day 3,000,000 gun owners fly on domestic U.S. flights.
Suppose the probability a gun owner will mistakenly take a gun to the airport is 0.00001. What is the probability that tomorrow more than 35 domestic passengers will accidentally get caught with a gun at the airport?

Choose the closest answer.

a. 0.02
b. 0.91
c. 0.16
d. 0.84
e. 0.28
Mathematics
1 answer:
valentinak56 [21]3 years ago
8 0

Answer:

c. 0.16

Step-by-step explanation:

For each passenger there are only two possible outcomes. Either they are caught with a gun, or they are not. The probability of a passenger being caught with a gun is independent from other passengers. So we use the binomial probability distribution to solve this question.

However, we are working with samples that are considerably big. So i am going to aproximate this binomial distribution to the normal.

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 = 3000000, p = 0.00001

So

\mu = E(X) = np = 3000000*0.00001 = 30

\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{3000000*0.00001*(1-0.00001)} = 5.48

What is the probability that tomorrow more than 35 domestic passengers will accidentally get caught with a gun at the airport?

This probability is 1 subtracted by the pvalue of Z when X = 35. So

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

Z = \frac{35 - 30}{5.48}

Z = 0.91

Z = 0.91 has a pvalue of 0.8186

1 - 0.8186 = 0.1814.

The closest answer is:

c. 0.16

You might be interested in
The population of a country was estimated to be 1.114 x 10^8. On this day, the population of the world was 3.853 x 10^9.
Lelechka [254]

Step-by-step explanation:

To find how many people lived outside of the country we subtract:

3.853 × 10^{9} - 1.114  × 10^{8}  = 3.7146 ×

To find the percentage of people living inside the country, we divide:\frac{1.114 x10^{8}}{3.853 x10^{9}} =2.8913x10^{-2} percent or 2.89%.  Which is extremely small.

6 0
3 years ago
If each exterior angle of a regular polygon is 30°, find how many sides the polygon has & the measure of an
WITCHER [35]

Answer:

12 sides and measure of each interior angle is 150...

8 0
3 years ago
Read 2 more answers
Please help me with these questions
kaheart [24]

Answers:

1st pic:

a) 2

b) 2.5 or 2

2nd pic:

a) 4

b) 5

c) 9

3rd pic:

a) 5

b) 3

Note: I may not be correct on all of them. Some of them were confusing a little bit, so I just wanted to let you know. Please don't come after me in the comments if I am wrong with one of the answers. In reality, you should be doing this. Either way, I hope this helps! Please, please, PLEASE mark brainliest. I would really appreciate it. :)

8 0
3 years ago
Please Answer numbers 4 and 5<br> Due Tomorrow! Please Answer with Explanation ;) thank you
Aleks [24]

Answer:

Median is the middle number

Mean is the average

Step-by-step explanation:

for #4

order the tree heights from the least to greatest and the middle number would be your median. If you have an even amount (no middle) then add the two middle numbers and dived it by 2

for # 5

Add the numbers all up on a calculator then dived by the amount of numbers you added.

Really simple :)

Hope that helps!

7 0
3 years ago
Read 2 more answers
(Solve and write addition Equations) Zacarias and Paz together have $756.80. If Zacarias has $489.50, how much does Paz have? Wr
serious [3.7K]
$489.50+x=$756.80 

x=amount paz has.

756.80-489.50 = 267.3

so Paz has $267.30
4 0
3 years ago
Read 2 more answers
Other questions:
  • There are 28 students in a class. Sixteen of those students are boys. What percent of the class are girls? (Round to the nearest
    14·2 answers
  • SIMPLIFY THE EXPRESSION!!!!!!!!!!!!!!!!!!!!!!!!
    9·2 answers
  • What is the exact area of a circle with radius 5?
    8·2 answers
  • Including scholarships and financial aid, Brett has $28,000 to spend on
    11·1 answer
  • Y is inversely proportional to the cube of x. If Y = 3 when x = 2, find Y, when x is 3. Write a proportion. Solve for y. Show wo
    12·1 answer
  • [6-(3x2)]+4 Simplifying Expression
    8·1 answer
  • A chef cooks rice using a 1: 2 ratio of dry rice to water. Her recipe calls for 9.5 cups of dry rice.
    10·1 answer
  • Which function’s graph has a y-intercept of 1.5?
    7·1 answer
  • 7. Evaluate the expression ab for a = 8 and b=5.
    14·1 answer
  • In 2018 the population of the world was approximately 7500 000 000
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!