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
MatroZZZ [7]
3 years ago
12

A test to determine whether a certain antibody is present is 99.2​% effective. This means that the test will accurately come bac

k negative if the antibody is not present​ (in the test​ subject). The probability of a test coming back positive when the antibody is not present​ (a false​ positive) is 0.008. Suppose the test is given to six randomly selected people who do not have the antibody.
​(a) What is the probability that the test comes back negative for all six ​people?
​(b) What is the probability that the test comes back positive for at least one of the six ​people?
Mathematics
2 answers:
Tems11 [23]3 years ago
7 0

Answer:

a) 95.29% probability that the test comes back negative for all six ​people

b) 4.71% probability that the test comes back positive for at least one of the six ​people

Step-by-step explanation:

For each person who do not have the antibody and are given the test, there are only two possible outcomes. Either the test comes back negative, or it comes back positive. The probability of the test coming back negative for a person is independent of any other person. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

99.2​% effective

So p = 0.992

six randomly selected people

This means that n = 6

​(a) What is the probability that the test comes back negative for all six ​people?

This is P(X = 6).

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 6) = C_{6,6}.(0.992)^{6}.(0.008)^{0} = 0.9529

95.29% probability that the test comes back negative for all six ​people

​(b) What is the probability that the test comes back positive for at least one of the six ​people?

Either it comes negative for all six people, or it comes positive for at least one of them. The sum of the probabilities of these events is 100%. So

p + 95.29 = 100

p = 4.71

4.71% probability that the test comes back positive for at least one of the six ​people

tiny-mole [99]3 years ago
3 0
Help PLEASe!

Marcus has created a budget for his upcoming trip to the theme park. Admission is 40% of the budget. He plans to spend 32% of his money on food, 23% on souvenirs, and save 5% for emergencies. He knows the admission will be $6 less than he will spend on food and souvenirs. How much money will Marcus need to take to the park?

You might be interested in
Determine the type of triangle that is drawn below.
SashulF [63]

Answer:

equalateral

Step-by-step explanation:

hope this helps

5 0
2 years ago
How to solve this with tan<br> I need AB
sesenic [268]

Answer:

AB = 2.18 units

Step-by-step explanation:

\tan 52\degree =\frac{AB}{BC}  \\  \\ AB = BC \tan 52\degree \\  \\ AB = 1.7  \times 1.2799416322 \\  \\ AB = 1.7  \times 1.2799416322 \\  \\AB = 2.17590077 \\  \\ AB  \approx 2.18 \: units

5 0
3 years ago
2r/5+7r/15= rewrite the expression by collecting like terms
kramer
<span>2r/5+7r/15=
LCM=15
(15\5=3*2r=6r)
15\15=1*7r=7r
answer=6r+7r\15
answer=13r\15</span>
3 0
3 years ago
Read 2 more answers
what is the largest amount of postage in cents that cannot be made by using only 3 cent and 5 cent stamps?
NARA [144]

Answer: The largest you can't make is 7 cents.

Step-by-step explanation:

Once you get 3 consecutive amounts, you can get all larger ones just by adding 3 cent stamps.  So let's see what you can make:

1 no

2 no

3 yes

4 no

5 yes

6 yes

7 no

8 yes, and this will give you 11 14 17 etc

9 yes, and this will give you 12 15 18 etc

10 yes, and this will give you 13 16 19 etc.

7 0
3 years ago
Read 2 more answers
Round off 53.96 to the nearest tenth​
Ne4ueva [31]

Answer:

54.0

Step-by-step explanation:

53.96

The bold number is in the tenth form and needs rounding off. So look at the number after the bold number (6).

Now 6 falls off the 5 or greater category, meaning that you have to add one to the bold number.

9 + 1 = 10

Now since the number is 10, you add the number before the bold number by 1 (underlined number) and replace the bold number by 0.

5<u>3</u>.96

54.00

Since you are focusing on the tenth place, keep the zero sitting on that spot.

54.0

5 0
2 years ago
Other questions:
  • Beverages inc. sells espresso for 8.50 per pound and roasted coffee for 10.25 per pound. the following equations represent a rec
    6·2 answers
  • Simplified form of -3a5-(-2a5)
    8·2 answers
  • Two random question! :)
    8·2 answers
  • QM Q9.) Write the standard form of the equation of the circle with the given center and radius.
    15·1 answer
  • Which situation could not be represented by the inequality below:
    8·2 answers
  • If 7 units equals to 98 liters, how many liters will 15 units have?
    9·2 answers
  • Can anyone help pls!!!!
    12·2 answers
  • Please help thanks I appreciate it! :)
    14·1 answer
  • What is the value of x?<br> Enter your answer in the box.<br> X=
    6·1 answer
  • What is the name of this line?
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!