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
avanturin [10]
2 years ago
14

Assume that each time a metal detector at an airport signals, there is a 25% chance that the cause is change in the passenger's

pocket. During a given hour, 15 passengers are stopped because of a signal from the metal detector. a) Find the probability that at least 3 passengers will have been stopped due to change in their pockets. b) If 15 passengers are stopped by the detector, would it be unusual for none of these to have been stopped due to change in the pocket
Mathematics
1 answer:
Neko [114]2 years ago
6 0

Answer:

a) 0.7639 = 76.39% probability that at least 3 passengers will have been stopped due to change in their pockets.

b) 0 is less than 2.5 standard deviations from the mean, so it would not be unusual.

Step-by-step explanation:

For each passenger, there are only two possible outcomes. Either they will have been stopped due to a change in the pocket, or not. Passengers are independent. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

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

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

And p is the probability of X happening.

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)}

A measure is considered unusual if it is more than 2.5 standard deviations of the mean.

25% chance that the cause is change in the passenger's pocket.

This means that p = 0.25

During a given hour, 15 passengers are stopped because of a signal from the metal detector.

This means that n = 15

a) Find the probability that at least 3 passengers will have been stopped due to change in their pockets.

This is

P(X \geq 3) = 1 - P(X < 3)

In which

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

So

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

P(X = 0) = C_{15,0}.(0.25)^{0}.(0.75)^{15} = 0.0134

P(X = 1) = C_{15,1}.(0.25)^{1}.(0.75)^{14} = 0.0668

P(X = 2) = C_{15,2}.(0.25)^{2}.(0.75)^{13} = 0.1559

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0134 + 0.0668 + 0.1559 = 0.2361

P(X \geq 3) = 1 - P(X < 3) = 1 - 0.2361 = 0.7639

0.7639 = 76.39% probability that at least 3 passengers will have been stopped due to change in their pockets.

b) If 15 passengers are stopped by the detector, would it be unusual for none of these to have been stopped due to change in the pocket

First we find the mean and the standard deviation:

E(X) = np = 15*0.25 = 3.75

\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{15*0.25*0.75} = 1.68

3.75 - 2.5*1.68 = -0.45

0 is less than 2.5 standard deviations from the mean, so it would not be unusual.

You might be interested in
Find the missing coordinate to complete the ordered pair.
MA_775_DIABLO [31]
(9,-4) you have to plugin 9 to the equation in the form of x. Then you add 5 and that would be your y value
8 0
3 years ago
Sam has 100 feet of fencing. Does he have enough fencing to enclose a circular region whose area is 630 square feet? Show work!
slavikrds [6]
A=pi(radius^2)
630/3.14=200.64
radius=14.16 feet
C=2(pi)(radius)
=3.14(2)(14.16)
=6.28(14.16)
C=88.92
88.92<100
Yes! He has enough fencing to enclose the circular area.
6 0
3 years ago
What is the range for the scores: 13, 23, 60, 46, 53, 75.
vova2212 [387]
Hello there.

Question: <span>What is the range for the scores: 13, 23, 60, 46, 53, 75.

Answer: Range is the largest value minus the smallest answer:
75 - 13 = 62.
The range is 62.

Hope This Helps You!
Good Luck Studying ^-^</span>
6 0
3 years ago
Which of the following is an equation of the line through (3, -1) and (−2, 14)?
enot [183]
D.
Slope is rise over run and in this case it is -15/ 5 so when it is reduced you get -3 as your slope
5 0
3 years ago
Read 2 more answers
Y=4x-18<br><br> Find ordered pairs of intercepts of each line
Masja [62]

The ordered pairs for the intercepts are as follows:

x intercept = 9/2

y intercept = -18

In order to find either of these you must put 0's in for the other variable. So, to find the x intercept, we start by putting 0 in for y.

y = 4x - 18

0 = 4x - 18

-4x = -18

x = 9/2

To find the y intercept, we put a 0 in for x.

y = 4x - 18

y = 4(0) - 18

y = 0 - 18

y = -18

5 0
3 years ago
Other questions:
  • kendrey ran 9 miles in 1 hour and 30 minutes. how long will it take her to run 12 miles at this pace?
    14·1 answer
  • Pamela makes cloth dolls, which she sells to friends and relatives. her total inventory includes over 200 yards of fabric, 100 y
    7·1 answer
  • If f(a) = 3a? – a, then what is the value of f(-2) ?
    13·1 answer
  • Jenny's frying pan has a radius of 8 inches. Find a. the circumference of the frying pan and b. the area of the frying pan. Use
    6·1 answer
  • Which expression is equivalent to −(4−3)?Which expression is equivalent to −(4−3)?
    10·2 answers
  • David bought 4.75 pounds of chicken for $11.40.
    12·2 answers
  • (4x – 17)<br> (5x - 1)<br><br> What is x?
    6·1 answer
  • Given the arithmetic sequence shown below, write a recursive rule for the sequence. -4,4,12, 20,​
    5·1 answer
  • 12. Use the geometric mean to find the 7th term in a geometric sequence if the 6th term is 8 and the 8th term is 18.
    12·1 answer
  • Please I need help the question is angle sum theorem
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!