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]
3 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]3 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
Translate the given phrase to an expression. Subtract 2/7 from 25/28. Do not simplify
erastova [34]
25/28 - 2/7
it doesn’t need to be solved because it asked for an expression and not an equation, so no equal sign either
6 0
3 years ago
Read 2 more answers
Answer pls fast<br><br> FIND ALL ANSWERS
-BARSIC- [3]

Answer:

ebhats

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Unknown angle problems (with algebra)
lubasha [3.4K]
Answer: x = 20 degree
3x = 3×20 which is 60 degree
And the other one is 100 degree
Add all the number 100+60+20 degree is 180 degree
7 0
3 years ago
3x3x3x11x11x__? = 16 335
kodGreya [7K]
Let the unknown number be y;

3×3×3×11×11×y = 16335;
3267×y = 16335;
y = 16335/3267;
y = 5;
5 0
3 years ago
Read 2 more answers
At the ice cream parlor,sundaes cost $4.25 and waffle cones cost $3.75.You and your friends have $50 to spend.Your group buys 5
stich3 [128]

Answer:

You can buy 7 waffle cones.

Step-by-step explanation:

Let sundae = x

Let waffle cones = y

4.25x + 3.75y ≤ 50

4.25 (5) + 3.75y ≤ 50

21.25 + 3.75y ≤ 50

3.75y ≤ 28.75

y ≤ 7.666666666

* round to the nearest whole to get 7

6 0
3 years ago
Other questions:
  • 7) Find the slope of the graph of the equation 3x+15y=25.<br><br> *Plz, Plz, Plz show your work.*
    11·1 answer
  • The domain of f(x) is {-1,0,2}. if f(x)=3x+2, what is the range
    14·1 answer
  • Suppose we have a population of N and we want to select a random sample of size n without replacement. What is the probability t
    7·1 answer
  • Suppose each bag costs 14.99. Estimate the total cost of 5 bags
    10·2 answers
  • 5x-3=13-3x how do I find x?
    8·2 answers
  • What is -5-3(-5x-3)-3x
    13·2 answers
  • What is the probability of rolling a number greater than 2 with a standard number cube
    12·1 answer
  • Help Pls Fast! (55 POINTS!)
    6·2 answers
  • What shows a example of symmetry?
    12·2 answers
  • What is ur mom plus ur dad
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!