Guidance Missile System A missile guidance system has ten fail-safe components. The probability of each failing is 0.40. Assume the variable is binomial. F the following probabilities. Round your answers to at least four decimal places. (a) Exactly eight will fail. P(exactly eight will fail)= 0.011 (b) More than eight will fail. P(more than eight will fail) = 4

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ISBN:9780470458365
Author:Erwin Kreyszig
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**Guidance Missile System**

A missile guidance system has ten fail-safe components. The probability of each failing is 0.40. Assume the variable is binomial. Find the following probabilities. Round your answers to at least four decimal places.

**Part 1:**

(a) Exactly eight will fail.

\[ P(\text{exactly eight will fail}) = 0.011 \]

(b) More than eight will fail.

\[ P(\text{more than eight will fail}) = \]

**Instructions:**

- Use the binomial probability formula to find the required probabilities.
- Ensure to round your answers to four decimal places for accuracy.
- Utilize a calculator or statistical software as needed.
Transcribed Image Text:**Guidance Missile System** A missile guidance system has ten fail-safe components. The probability of each failing is 0.40. Assume the variable is binomial. Find the following probabilities. Round your answers to at least four decimal places. **Part 1:** (a) Exactly eight will fail. \[ P(\text{exactly eight will fail}) = 0.011 \] (b) More than eight will fail. \[ P(\text{more than eight will fail}) = \] **Instructions:** - Use the binomial probability formula to find the required probabilities. - Ensure to round your answers to four decimal places for accuracy. - Utilize a calculator or statistical software as needed.
Expert Solution
Step 1

a Given that p=0.40.

n=10

Now,

q=1-p=1-0.40=0.60

Hence, q=0.60.

Pexactly eight will fail=C8np8q2=C8100.4080.602=10!8!108!0.4080.602=0.01060.011

Hence, Pexactly eight will fail=0.011.

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