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
8090 [49]
3 years ago
13

According to a​ survey, 65​% of murders committed last year were cleared by arrest or exceptional means. Fifty murders committed

last year are randomly​ selected, and the number cleared by arrest or exceptional means is recorded. When technology is​ used, use the Tech Help button for further assistance. ​(a) Find the probability that exactly 41 of the murders were cleared. ​(b) Find the probability that between 36 and 38 of the​ murders, inclusive, were cleared. ​(c) Would it be unusual if fewer than 18 of the murders were​ cleared? Why or why​ not?
Mathematics
1 answer:
monitta3 years ago
6 0

Answer:

a) P(X=41)=(50C41)(0.65)^{41} (1-0.65)^{50-41}=0.00421

b) P(X=36)=(50C36)(0.65)^{36} (1-0.65)^{50-36}=0.0714

P(X=37)=(50C37)(0.65)^{37} (1-0.65)^{50-37}=0.0502

P(X=38)=(50C38)(0.65)^{38} (1-0.65)^{50-38}=0.0319

And adding these values we got:

P(36 \leq X \leq 38)= 0.1535

c) We can find the expected value given by:

E(X) = np =50*0.65 = 32.5

And the standard deviation would be:

\sigma = \sqrt{np(1-p)} \sqrt{50*0.65*(1-0.65)}= 3.373

We can use the approximation to the normal distribution and we have at leat 95% of the data within 2 deviations from the mean. And the lower limit for this case would be:

\mu -2\sigma = 32.5- 2*3.373 = 25.75

And then we can consider a value of 18 as unusual lower for this case.

Step-by-step explanation:

Let X the random variable of interest "number cleared by arrest or exceptional", on this case we can model this variable with this distribution:

X \sim Binom(n=50, p=0.65)

The probability mass function for the Binomial distribution is given as:

P(X)=(nCx)(p)^x (1-p)^{n-x}

Where (nCx) means combinatory and it's given by this formula:

nCx=\frac{n!}{(n-x)! x!}

Part a

We want this probability:

P(X=41)=(50C41)(0.65)^{41} (1-0.65)^{50-41}=0.00421

Part b

We want this probability:

P(36 \leq X \leq 38)

We can find the individual probabilities:

P(X=36)=(50C36)(0.65)^{36} (1-0.65)^{50-36}=0.0714

P(X=37)=(50C37)(0.65)^{37} (1-0.65)^{50-37}=0.0502

P(X=38)=(50C38)(0.65)^{38} (1-0.65)^{50-38}=0.0319

And adding these values we got:

P(36 \leq X \leq 38)= 0.1535

Part c

We can find the expected value given by:

E(X) = np =50*0.65 = 32.5

And the standard deviation would be:

\sigma = \sqrt{np(1-p)} \sqrt{50*0.65*(1-0.65)}= 3.373

We can use the approximation to the normal distribution and we have at leat 95% of the data within 2 deviations from the mean. And the lower limit for this case would be:

\mu -2\sigma = 32.5- 2*3.373 = 25.75

And then we can consider a value of 18 as unusual lower for this case.

You might be interested in
Can a triangle be formed with the side lengths of 2.9 in, 4.8 in, and 7.4 in?
ddd [48]

Answer: Yes

Step-by-step explanation: A triangle can be formed because A+B>C

A and B are 2.9 and 4.8

Since those numbers have the least value

I added both and found that A and B are equal to 7.7

7.7>7.4

These sides could form a triangle

6 0
3 years ago
Explain how you know that21/30 is greater than 2/3
JulijaS [17]
You can divide 21 by 30 and that would give you 0.7 and if you divide 2 by 3 that would give you 0.6 repeating. Therefore, that is how I know that 21/30 is greater than 2/3.
4 0
3 years ago
Read 2 more answers
Mrs. Lowe, Mrs. Thomson and Ms. Rebuck went out to a restaurant for lunch. They each ordered a meal with a drink. Their total bi
rjkz [21]

Answer:

12.5

Step-by-step explanation:

use a calculator and don't waste your coins

6 0
2 years ago
Proof:<br> Given: Isosceles trapezoid TRAP with TR=PA<br> Prove: Angle RTA = angle APR
andre [41]
The answer is in the attachment

7 0
2 years ago
Are any of the wave heights considered an outliner
Fiesta28 [93]
Yes, the 10 foot wave is the outlier.
4 0
2 years ago
Other questions:
  • What answer to 1+7v+9
    11·2 answers
  • Michelle has an area in her garden for some plants and she wants to plant both tomatoes and bell peppers she can purchase tomato
    6·1 answer
  • Additive inverse of 1/3
    13·2 answers
  • Guys plssssssss! I want to spend time today and tomorrow with my fam before they go back to Washington
    9·2 answers
  • Write a polynomial function of least degree that has real coefficients, the following zeros: 1,5,3+i and a leading coefficient o
    9·1 answer
  • PLEASE HURRY WILL GIVE BRAILIEST!!
    7·2 answers
  • What do I have to do to find m
    9·1 answer
  • Anyone know the volume of this shape?
    5·1 answer
  • Please see all the screenshots. I have included multiply problems in this one question.
    8·1 answer
  • A professor has 7 books they are trying to arrange on a shelf. If the professor selects 3 books at a time, how many different ar
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!