Question

It is known that there is a defective chip on a computer board
that contains 8 chips. A technician tests the chips one at a time
until the defective chip is found. Assume that the chip to be
tested is selected at random without replacement. Let the random
variable *X*

denote the number of chips tested. What is the mean of
*X*?

Answer #1

Here there is a defective chip on a computer board that contains 8 chips. A technician tests the chips one at a time until the defective chip is found. Assume that the chip to be tested is selected at random without replacement.

Let the random variable *X* denote the number of chips
tested.

so here as we can that X can take values from 1 to 8.

p(x = 1) = P(First selected chip is a defective chip) = 1/8

p(x = 2) = P(Good chip selected as first chip) * P(Second chip selected is bad chip) = 7/8 * 1/7 = 1/8

similalry,

P(x) = 1/8 ; x = 1,2,3,4,5,6,7,8

Mean of X = E[x] = 1/8 * (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8) =
**4.5**

A box consists of 16 components, 6 of which are
defective.
(a)
Components are selected and tested one at a time, without
replacement, until a non-defective component is found. Let
X be the number of tests required. Find
P(X = 4).
(b)
Components are selected and tested, one at a time without
replacement, until two consecutive non defective
components are obtained. Let X be the number of tests
required. Find P(X = 5).

A lot of 106 semiconductor chips contains 29 that are defective.
Round your answers to four decimal places (e.g.
98.7654).
a) Two are selected, at random, without replacement, from the
lot. Determine the probability that the second chip selected is
defective.
b) Three are selected, at random, without replacement, from the
lot. Determine the probability that all are defective.

A lot of 101 semiconductor chips contains 25 that are
defective.
(a)
Two are selected, one at a time and without replacement from
the lot. Determine the probability that the second one is
defective.
(b)
Three are selected, one at a time and without replacement. Find
the probability that the first one is defective and the third one
is not 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?

A batch of 125 lightbulbs contains 13 that are defective. If
you choose 8 at random
(without replacement), what is the probability that
(a) None are defective?
(b) Exactly one is defective?
(c) More than 2 are defective?
whats needed
1) Define a random variable in words. (e.g. X = number of
heads observed)
2) Specify the distribution of the random variable including
identifying the value(s) of any
parameter(s). (e.g. X ∼ Binomial(10, 5))
3) State the desired probability in...

A certain brand of memory chip is likely to be defective with
probability p = 1/10. Let X be the number of defective chips among
n = 100 chips selected at random.
(a) (4 points) Find P(6 ≤ X ≤ 17) exactly. (Note: You only need
to provide a formal expression using the probability mass function
in this part, as the numerical value is beyond the range of the
table.)
(b) (4 points) Find P(6 ≤ X ≤ 17) using...

In a shipment of 20,000 toys (called robot chickens) 600 of
the toys are defective. Suppose that 20 toys are selected at random
(without replacement) for inspection, and let X denote the number
of defective toys found.
a) The distribution of the random variable X is (choose
one)
i) Binomial
ii) hypergeometric
iii) Poisson
iv) Normal
v) Exponential
vi) Uniform
b) Find P(X≤6).
c) Which distribution from those listed in part (a) can be
used as an approximation to the...

In a shipment of 20,000 toys (called robot chickens) 600 of the
toys are defective. Suppose that 20 toys are selected at random
(without replacement) for inspection, and let X denote the number
of defective toys found.
a) The distribution of the random variable X is (choose one)
i) Binomial
ii) hypergeometric
iii) Poisson
iv) Normal
v) Exponential
vi) Uniform
b) Find P(X≤6).
c) Which distribution from those listed in part (a) can be used
as an approximation to the...

A computer chip manufacturer tests a random sample of 500 chips
in a 4000 lot and finds 32 defective units.
a) Find a 95% confidence interval to estimate the proportion of
defective units and calculate the margin of error for your
estimate.
b) Find a 95% confidence interval to estimate the total number of
defective units and calculate the margin of error for your
estimate.
Answers:
a. [0.04393,0.08407], m.e. = 0.02, b. [175,337], m.e. = 81

Let a bowl contain 30 chips of the same size and shape. Only
one of those chips is red. Continue to draw chips from the bowl,
one at a time at random and without replacement, until the red chip
is drawn.
(a) Find the p.m.f. of X, the number of trials needed to draw
the red chip. Show your work.
(b) Compute the mean and variance of X. Show your work.
(c) Determine P( X less than or equal to...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 2 minutes ago

asked 14 minutes ago

asked 15 minutes ago

asked 26 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago