Question

Judging from recent experience, 5 percent of the computer keyboards produced by an automatic, high-speed machine...

Judging from recent experience, 5 percent of the computer keyboards produced by an automatic, high-speed machine are defective. If six keyboards are randomly selected, what is the probability that none of the keyboards are defective?
  • 0.001
  • 0.167
  • 0.735
  • 0.500
0 0
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Answer #1
Concepts and reason

A binomial distribution describes the possible number of times that a particular event will occur in a sequence of observations.

• A trial has only two possible outcomes namely success or failure.

• There is fixed number п
of identical trials.

• The trials of the experiment are independent of each other.

Fundamentals

The probability mass function of Binomial distribution is,

-)r-pr
Р(х -х)
p* (1-p)
х

Here,

п3
The number of trials

р
The probability of success

q1-p
The probability of failure

From the given information we have,

Sample size п-6

Probability of success is p 5%(or)0.05

Let X be the number of defective keyboards. Here X Binom(n 6,p 0.05)

The probability mass function is given by,

P(X x)
|(0.05) (1-0.05) ;x=0,1,....6
x

Compute the probability that none of the keyboards are defective. That is, P(х - 0)

(x-0)=(J00s(-03*
)(1-0.0s)
)(0.95
=1x1x0.7351
0.7351

Ans:

The probability that none of the keyboards are defective is 0.7351.

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