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NikAS [45]
3 years ago
14

The National Vaccine Information Center estimates that 90% of Americans have had chickenpox by the time they reach adulthood.32

(a) Suppose we take a random sample of 100 American adults. Is the use of the binomial distribution appropriate for calculating the probability that exactly 97 out of 100 randomly sampled American adults had chickenpox during childhood
Mathematics
1 answer:
drek231 [11]3 years ago
8 0

Answer:

0.59% probability that exactly 97 out of 100 randomly sampled American adults had chickenpox during childhood.

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they have had chickenpox, or they have not. The probability of a person having had chickenpox is independent from other people. So we use the binomial probability distribution to solve this problem.

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.

90% of Americans have had chickenpox by the time they reach adulthood.

This means that p = 0.9

Suppose we take a random sample of 100 American adults. Is the use of the binomial distribution appropriate for calculating the probability that exactly 97 out of 100 randomly sampled American adults had chickenpox during childhood

This is P(X = 97) when n = 100. So

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

P(X = 97) = C_{100,97}.(0.9)^{97}.(0.1)^{3} = 0.0059

0.59% probability that exactly 97 out of 100 randomly sampled American adults had chickenpox during childhood.

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Match the information on the left with the appropriate equation on the right.
kiruha [24]

Answer:

See attachment below

Step-by-step explanation:

For the first option, we are given m = - 2 / 3, b = 3. This is likely in the point - slope form y = mx + b, where m = slope and b = y - intercept. Thus, the equation of the line in point - slope form given this information, should be y = - 2 / 3x + 3. It seems as if none of the following equations match this form, so let us interchange the equation a bit,

y = - 2 / 3x + 3,

y + 2 / 3x = 3,

2x + 3y = 9 - Option C

_______________________________________________________

Next we are given m = - 3 / 2, and that this line passes through the point ( 4, - 1 ). Substitute m as - 3 / 2, x as 4, y as - 1, knowing point ( 4, - 1 ), into the form y = mx + b - solving for b.

- 1 = ( - 3 / 2 )( 4 ) + b,

b = 5,

Thus the equation in point - slope form should be y = - 3 / 2x + 5. None of the choices match this, so let us again alter the equation,

y = - 3 / 2x + 5,

2y = - 3x + 10,

- 2y = 3x - 10 - Option A

_______________________________________________________

( 6, 3 ) and ( 3, 1 ) is given to lie on this line. The slope of the line should be as follows,

Slope = 3 - 1 / 6 - 3 = 2 / 3

Now let us determine the y - intercept ( b ) by substitute one of the points, say ( 6, 3 ). In this case x = 6, and y = 3,

3 = ( 2 / 3 )( 6 ) + b,

b = - 1,

y = 2 / 3x - 1 = Option D

Take a look at the attachment below for further help;

3 0
3 years ago
Help please! Question is in picture
netineya [11]

39 ft of carpet

11x3+3x2=39

3 0
3 years ago
The graph shows a reflection in the x-axis. The matrix M such that, for any point (x, y), M(x, y) = (x', y') is
Rashid [163]

Answer:

This is a reflection about the x-axis.


Step-by-step explanation:

A reflection about the x-axis has the rule

[x,y]-> [x,-y].

Therefore

M[x,y] = [x,-y}

Let M=

|a  b|

|c  d|

Then the matrix multiplication gives

ax+by=x.............(1)

cx+dy=-y............(2)

Solving the previous equations (1) and (2) gives

a=1, b=0

c=0, d=-1

giving M as

|1  0|

|0 -1|


4 0
3 years ago
What is the result when the number 35 is increased by 20%?<br> Show me your work!
nirvana33 [79]

Answer:

42

Step-by-step explanation:

first we calculate what is 20% of 35 is then we add it to 35 to find the increased number

35 ÷ 100 = 0.35 this multipled by 20 = 7

35 + 7 = 42

3 0
3 years ago
A function has the function rule y = x - 7. If the input is 4, what is the output?
Troyanec [42]

Answer:

-3

Step-by-step explanation:

7 0
2 years ago
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