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bearhunter [10]
3 years ago
15

The National Center for Health Statistics (NCHS) reports that 70%70% of U.S. adults aged 6565 and over have ever received a pneu

mococcal vaccination. Suppose that you obtain an independent sample of 2020 adults aged 6565 and over who visited the emergency room and the pneumococcal vaccination rate applies to the sample. Determine the probability that exactly 12 members of the sample received a pneumococcal vaccination. Let XX represent the number of successes in a binomial setting with nn trials and probability pp of success in each trial. The probability of obtaining exactly kk successes is given by the formula
Mathematics
1 answer:
Marianna [84]3 years ago
3 0

Answer:

11.44% probability that exactly 12 members of the sample received a pneumococcal vaccination.

Step-by-step explanation:

For each adult, there are only two possible outcomes. Either they received a pneumococcal vaccination, or they did not. The probability of an adult receiving a pneumococcal vaccination is independent of other adults. 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.

70% of U.S. adults aged 65 and over have ever received a pneumococcal vaccination.

This means that p = 0.7

20 adults

This means that n = 20

Determine the probability that exactly 12 members of the sample received a pneumococcal vaccination.

This is P(X = 12).

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

P(X = 12) = C_{20,12}.(0.7)^{12}.(0.3)^{8} = 0.1144

11.44% probability that exactly 12 members of the sample received a pneumococcal vaccination.

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Todd has twice as many songs in his playlist as Vlad. Becca has three times as many songs in her playlist as Todd. If all three
nikitadnepr [17]

Answer:

Todd has 540540 songs in his playlist.

Vlad has 270270 songs in his playlist.

Becca has 162162 songs in her playlist.

Step-by-step explanation:

# of songs Todd has = T

# of songs Vlad has = V

# of songs Becca has = B

1) Todd has twice as many songs in his playlist as Vlad:

T=2V

2) Becca has three times as many songs in her playlist as Todd:

B=3T

3) All three people have a total of 243243 songs in their playlists:

T+V+B=243243

Because T=2V then you can substitute T as 2V in the second equation:

B=3(2V)

B=6V

Now in the final equation, you can substitute everything for V:

2V+V+6V=243243

9V=243243

V=27027

Now substitute for T:

T+1/2T+3T=243243

9/2T=243243

T=54054

Now substitute for B:

1/3B+1/6B+B=243243

3/2B=243243

B=162162

Check answers:

27027+54054+162162=243243

243243=243243

3 0
2 years ago
Solve the linear equation. 8x+32=2(25x−15)−11x8x+32=2(25x−15)−11x
Bogdan [553]
It seems like you put the same equation up there twice, but no worries! :)

8x + 32 = 2(25x - 15) - 11x

Simplify.

8x + 32 = 50x - 30 - 11x

Add like terms.

8x + 32 = (50x - 11x) - 30

Simplify.

8x + 32 = 39x - 30

Now we must subtract 32 from both sides.

8x = 39x - 30 - 32

Then, subtract 39x from both sides.

8x - 39x = -30 - 32

Simplify.

-31x = -62

Finally, divide both sides by -31.

-31x ÷ -31 = -62 ÷ -31

Simplify.

x = 2

~Hope I helped!~

8 0
3 years ago
.At Phil’s work, there are 12 part-time workers and 18 full-time workers. What is the ratio of part-time workers to total worker
Scrat [10]

Answer:

  2/5

Step-by-step explanation:

The desired ratio is ...

  (part-time)/(total) = (part-time)/((part-time) +(full-time)) = 12/(12+18)

  = 12/30 = 2/5

The ratio of part-time workers to total workers is 2 : 5.

7 0
3 years ago
John is paid 5% commission on the value of photocopiers he sells. Last week he sold $24,000 worth of copiers. He decided to inve
allsm [11]

Answer:

5040

Step-by-step explanation:

24000-5%=1200

1200+5%=1260

1260x4=5040

3 0
3 years ago
Which of the following is not a correct description of the graph of the function y = -2x - 7?
swat32
The graph of the function contains the points (0,-7), (1,-9), and (3,-1) is incorrect

it contains all the points except the last set...(3,-1)
y = -2x - 7
-1 = -2(3) - 7
-1 = -6-7
-1 = - 13 (incorrect)
7 0
3 years ago
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