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
svetlana [45]
3 years ago
13

According to a study done by Nick Wilson of Otago University Wellington, the probability a randomly selected individual will not

cover his or her mouth when sneezing is 0.267. Suppose you sit on a bench in a mall and observe people's bad habits as they sneeze.a. What is the probability that among 10 randomly observed individuals exactly 4 do not cover their mouth when sneezing?b. What is the probability that among 10 randomly observed individuals fewer than 3 do not cover their mouth when sneezing?c. Would you be surprised if, after observing 18 individuals, fewer than half covered their mouth when sneezing? why?
Mathematics
1 answer:
Lorico [155]3 years ago
3 0

Answer and Step-by-step explanation:

From the question statement we get know that it is Binomial distribution because there are only two possible outcomes so we need to use Binomial Probability Distribution for this question.

Formula for the Binomial Probability Distribution:

P(X)=   p^x q^(n-x)

Where,

  • C_x^n=n!/(n-x)!x!   (i.e. combination)
  • x= total number of successes
  • p=probability of success (p=1-q)  
  • q=probability of failure (q=1-p)
  • n=number of trials
  • P(X)= probability of total number of successes

Answer and explanation for each part of the question are as follow:

a.What is the probability that among 10 randomly observed individuals exactly 4 do not cover their mouth when sneezing?

Solution:

Given that

n=10  

p=0.267 (because p is the probability of success which is “number of individuals not covering their mouths when sneezing” in the question)

q=1-0.267=0.733  

x=4 (number of successes i.e. individuals not covering their mouths)

C_x^n=n!/(n-x)!x!=10!/(10-4)!4!=210

P(X)=C_x^n   p^x q^(n-x)=210×〖(0.267)〗^4×〖0.733〗^(10-4)

P(X)=210×0.00508×0.155  

P(X)=0.165465  

b. What is the probability that among 10 randomly observed individuals fewer than 3 do not cover their mouth when sneezing?

Solution:

Given that

n=10  

p=0.267 (because p is the probability of success which is “number of individuals not covering their mouths when sneezing” in the question)

q=1-0.267=0.733  

x=3 (number of successes i.e. individuals not covering their mouths)

C_x^n=n!/(n-x)!x!=10!/(10-3)!3!=120

P(X)=C_x^n   p^x q^(n-x)=120×(0.267)^3×〖0.733〗^(10-3)

P(X)=120×0.01903×0.1136  

P(X)=0.25962  

c. Would you be surprised if, after observing 18 individuals, fewer than half covered their mouth when sneezing? why?

Solution:

Given that

n=18  

p=0.267 (because p is the probability of success which is “number of individuals not covering their mouths when sneezing” in the question)

q=1-0.267=0.733  

x=9 (x is the number of successes “number of individuals not covering their mouths when sneezing”, if less than half cover their mouth then more than half will not cover), so let x=9

C_x^n=n!/(n-x)!x!=18!/(18-9)!9!=48620

P(X)=48620×(0.267)^9×〖0.733〗^(18-9)  

P(X)=48620×0.00000689×0.0610  

P(X)=0.020  

Yes, I am surprised that probability of less than 9 individuals covering their mouth when sneezing is 0.020. Which is extremely is small.

You might be interested in
5x^2-26x+5 factor the trinomial
ss7ja [257]
The factored form for this question is (5x-1)(x-5)
4 0
3 years ago
rosalyn has decided to purchase a $14,000 car . she plans on putting a $200 down toward the purchase, and financing the rest at
garik1379 [7]
$100 is the answer for your question
6 0
3 years ago
F(x)=3x-4 and g(x) = x2 find the value of f(3)-g(2) <br><br> show all work
zheka24 [161]

Answer: 1

f(x) = 3x - 4 => f(3) = 3.3 - 4 = 9 - 4 = 5

g(x) = x² => g(2) = 2² = 4

=> f(3) - g(2) = 5 - 4 = 1

Step-by-step explanation:

3 0
3 years ago
shayla has 6 1/2 pounds of potato salad she needs to away into containers. each container only hodls 1 5/8 pounds. how many cont
sergiy2304 [10]

Answer:

She will need 4 containers

Step-by-step explanation:

First turn the fractions into decimals, 6 1/2 turns into 6.5, and 1 5/8 turns into 1.625, then divide.

6.5 divided by 1.625 equals 4

6 0
3 years ago
Which inequalities are true plz help!!!
alex41 [277]

Answer:2,3, and 5

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
Other questions:
  • Sara, Nick and June share some sweets in the ratio 5:5:3. Sara gets 18 more sweets than June. How many sweets does Nick get?
    12·1 answer
  • A Chemist has 100g of 25% acid solution. How much of these solution he needs to drain and replace with 70% acid solution to obta
    8·2 answers
  • Werner's Deli can make 2.2 sandwiches
    8·1 answer
  • How can you tell if a number is divided by 4
    5·2 answers
  • Let f(x)=x^2-2x+1
    5·1 answer
  • solve each problem.simplify your answer.One inch on a map equals 375 miles.what do 5 3/4 inches represent.
    8·1 answer
  • HHHEEEEEELP PLEASE!!!! NEED ASAP!!!! HUUUURRRRYYYY
    14·1 answer
  • Indicate the method you would use to prove the two triangle 's . If no method applies, enter "none".
    8·2 answers
  • Mrs. Silverstein bought 3 mini cakes for a birthday party. She cuts each cake into quarters and plans to serve each guest 1 quar
    10·1 answer
  • Convert 3.5 into fraction​
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!