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
Arte-miy333 [17]
3 years ago
8

Consider the probability that exactly 20 out of 309 people will get the flu this winter. Choose the best description of the area

under the normal curve that would be used to approximate binomial probability.
Mathematics
1 answer:
noname [10]3 years ago
6 0

Answer:

The distribution of proportion of people who will get the flu this winter is <em>N</em> (0.065, 0.014²).

Step-by-step explanation:

Let <em>X</em> = number of people who will get flu this year.

The sample selected is of size, <em>n</em> = 309.

The number of people who will get flu in this sample is, <em>x</em> = 20.

Compute the sample proportion of people who will get flu as follows:

p=\frac{x}{n}=\frac{20}{309}=0.065

The random variable <em>X</em> follows a Binomial distribution with parameters <em>n</em> = 309 and <em>p</em> = 0.065.

The sample size is quite large, i.e. <em>n</em> = 309 > 30.

And the probability of success is low.

So the Normal approximation to Binomial can be used to approximate the distribution of sample proportion is:

  1. np ≥ 10
  2. n(1 - p) ≥ 10

Check whether the conditions are fulfilled or not as follows:

np=309\times 0.065=20.085>10\\n(1-p)=309\times (1-0.065)=288.915>10

Hence, the conditions are fulfilled.

The sampling distribution of sample proportion is:

p=N(p, \frac{p(1-p)}{n})

Compute the mean and variance as follows:

Mean=p=0.065\\Variance=\frac{p(1-p)}{n}=\frac{0.065(1-0.065)}{309}=0.014^{2}

Thus, the distribution of proportion of people who will get the flu this winter is <em>N</em> (0.065, 0.014²).

You might be interested in
Ellen is opening. Cookie shop eat a local middle school . She randomly surgery’s students to determine The types of cookies they
saw5 [17]

Complete Question:

Ellen is opening. Cookie shop eat a local middle school . She randomly surveys students to determine The types of cookies they would buy at the cookie shop the results of the surveys are below based on the survey. Which statement is not true?

A) If 160 students buy a cookie, approximately 18 students would buy a sugar cookie.

B) 22½% of the students surveyed would buy a sugar cookie.

C) If 240 students were to purchase a cookie from the store, approximately 66 students will purchase a peanut butter cookie.

D) Half of the students prefer chocolate chips or oatmeal raisin cookies.

(Table showing the results of her survey is in the attachment below)

Answer:

A) If 160 students buy a cookie, approximately 18 students would buy a sugar cookie.

Step-by-step Explanation:

STEP 1:

In order to ascertain which of the statements given in the options that is NOT TRUE, let's express the given number of students that would buy the different types of cookies in their PROPORTIONS AND PERCENTAGES in the survey result.

Thus:

Type of Cookie==> no of students => Proportion (no of students of a cookie type ÷ total no of students) => % (each proportion for a cookie type)

Chocolate Chip==> 25 => 0.3125 (25÷80) => 31.25% (0.3125 × 100)

Oatmeal Raisin==> 15 => 0.1875 (15÷850) => 18.75% (0.1875 × 100)

Peanut Butter== 22 => 0.275 (22÷80) => 27.5% (0.275 × 100)

Sugar ==> 18 => 0.225 (18÷80) => 22.5% (0.225 × 100)

STEP 2:

Next step is to consider each statement given in the question to see if they are true or not.

==>OPTION A: If 160 students buy a cookie, approximately 18 students would buy a sugar cookie.

To find out if this is true, multiply the proportion of students who would be buy a sugar cookie (0.255) by 160 = 0.255 × 160 = 36.

If 160 buy a cookie, approximately 36 students would buy a sugar.

Option A IS NOT TRUE.

OPTION B: 22½% of the students surveyed would buy a sugar cookie.

From our calculation in STEP 2, we have:

Sugar ==> 18 => 0.225 (18÷80) => 22.5% (0.225 × 100).

Option B is TRUE. 22.5% of the students would go for sugar cookie.

OPTION C: If 240 students were to purchase a cookie from the store, approximately 66 students will purchase a peanut butter cookie.

Number of students that would buy the peanut butter if 240 students were to get a cookie = proportion of students that opt for peanut butter cookie in the survey (0.275) × 240 = 0.275 × 240 = 66.

Option C is TRUE.

OPTION D: D) Half of the students prefer chocolate chips or oatmeal raisin cookies.

Proportion of students who prefer chocolate chips or oatmeal raisin cookies = 0.3125 + 0.1785 = 0.491

This is approximately 0.5 = ½ of the total number of students.

Option D is TRUE.

Therefore, we can conclude that the statement, "A) If 160 students buy a cookie, approximately 18 students would buy a sugar cookie" is NOT TRUE.

3 0
3 years ago
When drawing the arcs in order to bisect a line segment, why must the width of the compass be more than half of the length of
Aleonysh [2.5K]

Answer: Choice A

If the compass isn't open wide enough, then the arcs won't intersect forming the points we need to create the perpendicular bisector.

Check out this link to see my response to the identical question answered 2 days ago

brainly.com/question/17191122

feel free to ask any questions you have if you're still stuck

8 0
2 years ago
Help me please?!!!!!!!!!
Basile [38]
I think it’s the last one but I’m not sure
4 0
3 years ago
Read 2 more answers
Given cos 0 = 4V2/7, find sin 0.<br> sin 0 =<br> V[?]/?
zmey [24]

sin =  \frac{ \sqrt{17} }{7}

8 0
2 years ago
Which of the following equations describes the line shown below? Check all
Setler79 [48]

Answer:

y = -1/2 x + 2

Step-by-step explanation:

Which of the following equations describes the line shown below? Check all

that apply.

(-4, 4)

(2, 1)

The standard equation of a line is y = mx,+b

m is the slope

b is he y-inttercept

Get the slope

Slope m = y2-y1/x2-x1

Substitute the coordinate

M = 1-4/2-(-4)

M = -3/6

M = -1/2

Substitute m= -1/2 and (2,1) into y = mx+b

1 = -1/2(2)+b

1 = -1+b

b = 1+1

b=2

Get the equation

Recall y =mx+b

y = -1/2 x + 2

3 0
2 years ago
Other questions:
  • 1 5⁄7 ÷ 4 2⁄7 i need the anser im stuck
    6·2 answers
  • Solve the equation 1/2x=7/6
    9·2 answers
  • Polygon A B C D E F has 6 sides. Exterior angle A is 62 degrees, exterior angle B is 44 degrees, exterior angle C is 70 degrees,
    10·2 answers
  • Why are data organized into tables and graphs?
    9·2 answers
  • If I have 5$ and then I take away 4.99$ how much money do I have
    5·2 answers
  • Help asap ill mark brainlist
    14·1 answer
  • Please help answer correctly !!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!!!!!
    10·1 answer
  • What is the equation of the line that passes through the point (8, -8) and has a slope of -1
    6·1 answer
  • WHATS THE ANSWER HELP
    10·1 answer
  • You can drive 90 miles in 1/4 of a tank of gas in 1 hour.
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!