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18 percent of people in a city eligible to donate blood actually do. You randomly select four eligible blood donors and ask them if they donate blood. Complete parts​ (a) through​ (d) below.

Sagot :

MrRoyal

Answer:

[tex]P(x = 1) = 0.3970[/tex]

[tex]P(x = 2) = 0.1307[/tex]

[tex]P(x = 3) = 0.0191[/tex]

[tex]P(x = 4) = 0.0011[/tex]

Step-by-step explanation:

Given

[tex]n =4[/tex]

[tex]p = 0.18[/tex]

Required

(a) - (d)

x | P(x)

0 | 0.452

1 |

2 |

3 |

4 |

To solve (a) to (d), we simply apply the following binomial probability formula

[tex]P(x) = ^nC_xp^x(1-p)^{n-x}[/tex]

Solving (a):

[tex]x = 1[/tex]

So, we have:

[tex]P(x = 1) = ^4C_1 * (0.18)^1 * (1-0.18)^{4-1}[/tex]

[tex]P(x = 1) = ^4C_1 * (0.18)^1 * (1-0.18)^{4-1}[/tex]

[tex]P(x = 1) = 4 * (0.18)^1 * (1-0.18)^3[/tex]

[tex]P(x = 1) = 0.3970[/tex]

Solving (b):

[tex]x = 2[/tex]

So, we have:

[tex]P(x = 2) = ^4C_2 * (0.18)^2 * (1-0.18)^{4-2}[/tex]

[tex]P(x = 2) = 6 * (0.18)^2 * (1-0.18)^2[/tex]

[tex]P(x = 2) = 0.1307[/tex]

Solving (c):

[tex]x = 3[/tex]

So, we have:

[tex]P(x = 3) = ^4C_3 * (0.18)^3 * (1-0.18)^{4-3}[/tex]

[tex]P(x = 3) = 4 * (0.18)^3 * (1-0.18)^1[/tex]

[tex]P(x = 3) = 0.0191[/tex]

Solving (d)

[tex]x = 4[/tex]

So, we have:

[tex]P(x = 4) = ^4C_4 * (0.18)^4 * (1 - 0.18)^{4-4}[/tex]

[tex]P(x = 4) = 1 * (0.18)^4 * (1 - 0.18)^0[/tex]

[tex]P(x = 4) = 0.0011[/tex]

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