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weqwewe [10]
2 years ago
9

The probability of being a universal donor is 6% (O-negative-blood type). Suppose that 6 people come to a blood drive.' a) What

are the mean and standard deviation of the number of universal donors among the 6 people? b) What is the probability that there are exactly three universal donors?
Mathematics
1 answer:
Tcecarenko [31]2 years ago
7 0

Answer:

Mean = 0.36

SD = 0.5817

P(x=3) = 0.003588

Step-by-step explanation:

Given

Let

A = Event of being a universal donor.

So:

P(A) = 0.06

n = 6

Solving (a): Mean and Standard deviation.

The mean is:

Mean = np

Mean = 6 * 0.06

Mean = 0.36

The standard deviation is:

SD = \sqrt{np(1-p)}

SD = \sqrt{6*0.06*(1-0.06)}

SD = \sqrt{0.3384}

SD = 0.5817

Solving (b): P(x = 3)

The event is a binomial event an dthe probability is calculated as:

P(x) = ^nC_x * p^x * (1-p)^{n-x}

So, we have:

P(x=3) = ^6C_3 * 0.06^3 * (1-0.06)^{6-3}

P(x=3) = ^6C_3 * 0.06^3 * (1-0.06)^3

P(x=3) = 20 * 0.06^3 * (1-0.06)^3

P(x=3) = 0.003588

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