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Natalka [10]
1 year ago
15

Unknown to a medical researcher, 6 out of 25 patients have a heart problem that will result in death if they receive the test dr

ug. 8 patients are randomly selected to receive the drug and the rest receive a placebo. What is the probability that exactly 6 patients will die? Express your answer as a fraction or a decimal number rounded to four decimal places.
Mathematics
1 answer:
Fiesta28 [93]1 year ago
8 0

Using the hypergeometric distribution, it is found that there is a 0.0002 = 0.02% probability that exactly 6 patients will die.

<h3>What is the hypergeometric distribution formula?</h3>

The formula is:

P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}

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

The parameters are:

  • x is the number of successes.
  • N is the size of the population.
  • n is the size of the sample.
  • k is the total number of desired outcomes.

The values of the parameters for this problem are:

N = 25, k = 6, n = 8.

The probability that exactly 6 patients will die is P(X = 6), hence:

P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}

P(X = 6) = h(6,25,8,6) = \frac{C_{6,6}C_{19,2}}{C_{25,8}} = 0.0002

0.0002 = 0.02% probability that exactly 6 patients will die.

More can be learned about the hypergeometric distribution at brainly.com/question/24826394

#SPJ1

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People in Spaceland live in 8 space stations, and travel between the stations in tubes.Every pair of stations is connected by tw
NeTakaya

Based on the way these stations are connected, we can infer that there are <u>56 tubes. </u>

<h3>Number of tubes in Spaceland </h3>

Each pair of stations have 2 tubes. This means that every station is connected to each of the others.

We can therefore infer that each station has 7 tubes to the other stations.

The total number of tubes would therefore be:

= Number of stations x Number of tubes per station

= 8 x 7

= 56 tubes

In conclusion, there are 56 tubes.

Find out more on proportionality problems at brainly.com/question/24822176.

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2 years ago
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Last year, Adele went bowling several times and earned an average score of 95 points.
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Answer:

40 percent increase

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End point - 133

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A bank manager wants to encourage new customers to open accounts with principals of at least ​$2 comma 500. He decides to make a
prisoha [69]

Answer:

To earn $10 in 1st month, the principal must be $4,000.

No, the poster cannot claim that "Open an account of ​$2 comma 500 and earn at least ​$10 interest in 1​ month!".

Step-by-step explanation:

We have been given that a bank manager wants to encourage new customers to open accounts with principals of at least ​$2,500. He decides to make a poster advertising a simple interest rate of 3​%. We are asked to find the principal to advertise that one can earn ​$10 the first​ month.

We will use simple interest formula to solve our given problem.

I=Prt, where,

I = Amount of interest,

P = Principal amount,

r = Annual interest rate in decimal form,

t = Time in years.

r=3\%=\frac{3}{100}=0.03

1 month will be equal to \frac{1}{12}.

\$10=P\cdot0.03\cdot \frac{1}{12}

\$10=0.0025P

\frac{\$10}{0.0025}=\frac{0.0025P}{0.0025}

P=\$4000

Therefore, to earn $10 in 1st month, the principal must be $4,000.

Now, we will check if an account of ​$2,500 can earn at least ​$10 interest in 1​ month.

I=\$2500\cdot 0.03\cdot \frac{1}{12}

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Since the account earns an amount of $6.25 in one month, therefore, the poster is not true.

4 0
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