Question

**QUESTION 5- A factory produces pins of which 1.5% are
defective. The components are packed in boxes of 12. A box is
selected at random.**

(1) n =

(2) p = (Round to four decimal places)

(3) q = (Round to four decimal places)

Find the following probabilities (Round ALL answers to four decimal places):

4) The box contains exactly 6 defective pins

5) The box contains at least one defective pins

6) The box contains no more than two defective pins

7) The box contains between four and eight defective pins

8) All the pins in the box are defective

9) The box contains less than three or more than nine defective pins

10) The box contains no defective pins

11) The box contains less than eight or between five and ten defective pins.

12) The box contains less than seven

13) The box contains more than ten Calculate

(Round ALL answers to two decimal places):

14) The mean of the variable “the number of defective pins”.

15) The standard deviation of the variable “the number of defective pins”.

Answer #1

A factory produces components of which 1% are defective. The
components are packed in boxes of 10. A box is selected by
random.
a) Find the probability that there are at most 2 defective
components in the box.
b) Use a suitable approximation to find the probability of
having at most 3 defective (inclusive 3 cases) components out of
250.

A factory produces components of which 1% are defective. The
components are packed in boxes of 10. A box is selected by
random.
a) Find the probability that there are at most 2 defective
components in the box.
b) Use a suitable approximation to find the probability of
having at most 3 defective (inclusive 3 cases) components out of
250.

A tray of electronic components contains 22 components, 4 of
which are defective. If 4 components are selected, what is the
possibility of each of the following? (Round your answers to five
decimal places.)
(a) that all 4 are defective
(b) that 3 are defective and 1 is good
(c) that exactly 2 are defective
(d) that none are defective

Suppose that a box contains 6 pens and that 4 of them are
defective. A sample of 2 pens is selected at random without
replacement. Define the random variable XX as the number of
defective pens in the sample. If necessary, round your answers to
three decimal places.
Write the probability distribution for XX.
xx
P(X=xX=x)
What is the expected value of X?

The number of calls received by an office on Monday morning
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please show how you calculated your answers
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