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
Art [367]
3 years ago
6

We learned in Exercise 4.18 that about 90% of American adults had chickenpox before adulthood. We now consider a random sample o

f 120 American adults. (a) How many people in this sample would you expect to have had chickenpox in their childhood? And with what standard deviation? (b) Would you be surprised if there were 105 people who have had chickenpox in their childhood? (c) What is the probability that 105 or fewer people in this sample have had chickenpox in their childhood? How does this probability relate to your answer to part (b)?
Mathematics
1 answer:
liraira [26]3 years ago
4 0

Answer:

a) 108 people with a standard deviation of 3.286335

b) No

c) 0.218163 or around 21.82%

d) See explanation below.

Step-by-step explanation:

This situation can be modeled with the Binomial Distribution which gives t<em>he probability of an event that occurs exactly k times out of n, and is given by </em>

<em>\large P(k;n)=\binom{n}{k}p^kq^{n-k} </em>

<em>where  </em>

<em>\large \binom{n}{k}= combination of n elements taken k at a time. </em>

<em>p = probability that the event (“success”) occurs once </em>

<em>q = 1-p </em>

In this case, the event “success” is finding an American adult who had  chickenpox before adulthood with probability p=0.9

and n=120 American adults in the sample.

The <em>standard deviation for this binomial distribution</em> is

\large s=\sqrt{npq}

where <em>n is the sample size 120 </em>

a)

We consider a random sample of 120 American adults. How many people in this sample would you expect to have had chickenpox in their childhood?

If about 90% of American adults had chickenpox before adulthood, we expect to find 90% of 120 = 0.9*120=108 people in the sample who had chickenpox in their childhood.

The  standard deviation would be

\large s=\sqrt{120*0.9*0.1=3.286335}

b)

Would you be surprised if there were 105 people who have had chickenpox in their childhood?

No, because 105 and 108 are in the interval [mean - s, mean +s]

c)

What is the probability that 105 or fewer people in this sample have had chickenpox in their childhood?

The probability that 105 or fewer people in this sample have had chickenpox in their childhood is

\large \sum_{k=0}^{105}\binom{120}{k}0.9^k0.1^{120-k}

We compute this value easily with a spreadsheet and we get

\large \sum_{k=0}^{105}\binom{120}{k}0.9^k0.1^{120-k}=0.218163\approx 21.82\%

d)

How does this probability relate to your answer to part (b)?

A binomial distribution with np>5 and nq>5 with n the sample size as is the case here, behaves pretty much like a Normal distribution with mean np and standard deviation \large \sqrt{npq}, so around 60% of the data are in the interval  [mean -s, mean +s] and 40% outside, so roughly <em>20% of the data should be in [0, mean-s] </em>

You might be interested in
A convex hexagon has interior angles with measures x^0, (5x - 103); (2x + 60), (7x - 31), (6x -6), and (9x - 100), what is the v
cestrela7 [59]

Answer:

x = 30.66°

Step-by-step explanation:

The sum of the interior angles of a hexagon is 720°

Each angles are x^0, (5x - 103); (2x + 60), (7x - 31), (6x -6), and (9x - 100),

we add all these angles together

x^0 + (5x - 103) + (2x + 60) + (7x - 31) + (6x -6) + (9x - 100) = 720

x^0  = 1

1 + (5x - 103) + (2x + 60) + (7x - 31) + (6x -6) + (9x - 100)

1 + 5x - 103 +2x + 60 + 7x -31 + 6x - 6 + 9x - 100 = 720

1 - 103 + 60 - 31 - 6 - 100 + 5x + 2x + 7x + 6x + 9x = 720

1 - 180 + 29x = 720

-179 + 29x = 720

29x = 720 + 179 = 889

x = 889/29 = 30.655 ≅ 30.66°

3 0
3 years ago
PLEASE HELP WILL GIVE THE FIRST PERSON TO ANSWER BRAINLIEST!! In a target shooting contest, contestants receive 5 points for hit
vekshin1

Answer:

Tom hit 13 red targets!

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
How do you write 1.14 as a fraction
Alekssandra [29.7K]
1.14 = 1 \dfrac{14}{100}  = 1 \dfrac{14 \div 2}{100 \div 2}=  1 \dfrac{7}{50}
5 0
3 years ago
Edwin hiked to a famous point with a beautiful view. It took 2 hours and 55 minutes to hike to the viewpoint and 25 minutes to h
anygoal [31]

Answer:

= 8:00 A.M.

Step-by-step explanation:

▪You first find the total time taken which will be :

2 hrs 55 min + 25 min

= 3 hrs 20 min + 25 min

= 3 hrs 45min

▪ Beginning time = Arrival time - Time taken

= 11:45 - 3:45

= 8:00 am

¿

7 0
3 years ago
What does reflecting over each axis do to a function algebra 2
love history [14]
Gggggghhhhhbhhjnjjnjjjjjjjjjjjjjkk
6 0
3 years ago
Other questions:
  • A recent survey of 200 pet owners reveals that the ration of cat owners to dog owners in a city is 5 to 3. If there are 20,000 r
    10·1 answer
  • Find f(-2) for f(x) = 2*3^x
    5·2 answers
  • A group of students must collect at least $160 to organize a science fair. They have already collected $20. Which graph best rep
    10·2 answers
  • Find RA, 90: (2,5) given that point A is located at (-3, -3).
    11·1 answer
  • One side of equilateral triangle is represented with the expression-2x+8 and other 3x-2 find perimeter
    12·1 answer
  • a box shaped like a rectangular prism has a length of 8 inches and a width of 8 inches. its volume is 512 cubic inches. what is
    12·1 answer
  • you have a bag of marbles. 5 marbles are blue, 4 marbles are red, and 2 marbles are yellow. What is the probability that you pul
    5·1 answer
  • Hurry guys help0.04x61=
    7·2 answers
  • Write as an equation: a triangle has two equal sides and a third side that is 15cm long. How long is each of the equal sides if
    11·1 answer
  • A piece of machinery depreciates $6000 the first year,
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!