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A stragitic defense strategy calls for missiles to be fired independelty at a target until the target us hit. Let the probability that any missile will hit the target be .8 and x=# of missiles fired at the target

Respuesta :

MrRoyal

Points:

The question is incomplete as the value of x is not given and what is required is not stated.

However, I'll assume that x = 5

Going by the details of the question, possible questions could be:

  • Expected number of hits
  • Variance and Standard Deviation of hits

Answer:

See Explanation

Step-by-step explanation:

Given

Represent the probability with p.

So:

[tex]p = 0.8[/tex]

Solving (a): The expected number of hits.

In probability, the expected number is calculated as:

[tex]E(x) = p * x[/tex]

Substitute values for p and x

[tex]E(x) = 0.8 * 5[/tex]

Remember that 5 is an assumed value of x

[tex]E(x) = 4[/tex]

Hence, the expected number of hits when 5 missiles is fired is 4

Solving (b): Variance

In probability, variance is calculated as:

[tex]variance = x*p*(1-p)[/tex]

Substitute values for p and x

[tex]variance = 5*0.8*(1-0.8)[/tex]

[tex]variance = 5*0.8*0.2[/tex]

[tex]variance = 0.8[/tex]

Hence, the variance is 0.8

Solving (c): The standard deviation

In probability, the standard deviation is calculated as:

[tex]SD= \sqrt{Variance[/tex]

Substitute values for variance

[tex]SD= \sqrt{0.8[/tex]

[tex]SD= 0.89[/tex]

Hence, the standard deviation is 0.89

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