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
HELPP PLEASEE TELL ME WHICH IS RIGHT AND WRONG AND HELP KE EXPLAIN I DONT WANNA FAIL SUMMER SCHOOL NO LINKS OR FILE WOULD BE DEE
Alik [6]

Answer:

Orca Correct, Sea Star Wrong. Heart it if it was helpful :D

Step-by-step explanation:

11-4=7. Orca correct.

Sea star...11-4=7

Wrong its 7, not -7

7 0
3 years ago
Read 2 more answers
Which list shows all the factors of 54? A. 1, 2, 3, 6, 9, 12, 18, 27, 54 B. 1, 2, 3, 6, 9, 18, 27, 54 C. 1, 2, 3, 6, 9, 18, 54 D
sergey [27]

Answer:

C

Step-by-step explanation:

Bc I have Big Brain and Google is nice

6 0
3 years ago
Read 2 more answers
6x^2 - 2 and 6x^2 + 2
AlexFokin [52]
2+2= 4
Easy Peary leman squeaky
Good
7 0
3 years ago
Read 2 more answers
Please helpp <br> 25 = (a - 29/10
dedylja [7]

Step-by-step explanation:

If you like my answer than please mark me brainliest and follow me thanks

3 0
3 years ago
Workers on the assembly line produce 4x + 6 boats each day. Which expression shows how many boats they produced in 12 days?
Annette [7]
We're going to assume that x = # of days.
Plug 12 in as x:
4 × 12 = 48
48 + 6 = 54
They produced 54 boats in 12 days.
7 0
3 years ago
Read 2 more answers
Other questions:
  • Find the minimum value of the function for the polygonal convex set determined by the given system of inequalities.
    6·1 answer
  • What is the length of one leg of the triangle?
    15·1 answer
  • Find x such that 2x^2 +2x=12
    13·1 answer
  • The annount of time (in minutes) that it takes to put out a fire varies inversely
    7·1 answer
  • 1567÷135<br><br>plz help 50 points ​
    7·2 answers
  • Hector surveyed 500 people and asked them how far they drive to work and what is the last digit of their phone number. He used t
    10·1 answer
  • What is the scale of a drawing where a 36 foot tall statue is 9 inches tall?
    12·1 answer
  • Simple math
    11·1 answer
  • What is the value of t?
    14·1 answer
  • PLEASE HELPPPPP
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!