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Ganezh [65]
1 year ago
14

The centers for disease control and prevention reports 25% baby boys 6 to 8 months in the US weigh more than 20 pounds a sample

of babies 16 is studied what is the probability that fewer than three weigh more than 20 pounds?
Mathematics
1 answer:
Vesna [10]1 year ago
3 0

Answer:

P(x < 3) = 0.1971

Explanation:

To calculate the probability that x babies weigh more than 20 pounds, we will use the binomial distribution, so it can be calculated as:

\begin{gathered} P(x)=nCx\cdot p^x\cdot(1-p)^{n-x} \\ Where\text{ nCx=}\frac{n!}{x!(n-x)!} \\  \\ With\text{ n = size of sample} \\ p=\text{ probability of success \lparen the baby weight more than 20 pounds\rparen} \end{gathered}

So, replacing n = 16 and p = 0.25, we get that the probability is equal to

P(x) = 16Cx (0.25)^x (1 - 0.25)^(16 - x)

P(x)=16Cx\cdot0.25^x\cdot(1-0.25)^{16-x}

Now, the probability that fewer than three weights more than 20 pounds are equal to

\begin{gathered} P(x

Then

P(x < 3) = 0.01 + 0.0535 + 0.1336

P(x < 3) = 0.1971

Therefore, the answer is

P(x < 3) = 0.1971

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