Question

1-The number of defective components produced by a certain process in one day has a Poisson distribution with mean 19. Each defective component has probability 0.6 of being repairable.

a) Given that exactly 15 defective components are produced, find the probability that exactly 10 of them are repairable.

b) Find the probability that exactly 15 defective components are produced, with exactly 10 of them being repairable.

Answer #1

The distribution given here is:

a) The number of repairable components out of 15 defective ones could be modelled here as:

The required probability here is computed as:

**Therefore 0.1859 is the required probability
here.**

b) The probability that exactly 10 defective components are there with exactly 10 of them being repairable

**Therefore 0.0121 is the required probability
here.**

In a certain factory, Machine A makes 50% of the components,
with 1 in 15 being defective. Machine B produces 25%, with 1 in 10
being defective. Machine C produces the rest, with 1 in 20 being
defective.
(a) Complete the probability table for this scenario using the
given template.
(b) What is the probability that a defective component is
produced?
(c) If a component is selected at random and found to be
defective, what is the probability it was...

Data indicates that the number of traffic accidents on a rainy
day is Poisson with mean 19, while on a dry day, it is Poisson with
mean 13. Let X denote the number of traffic accidents tomorrow.
Suppose that the chance it rains tomorrow is 0.6. Find(a)P(rain
tomorrow|X= 15) using Bayes rule. (b)E(X).

1. Suppose that a shipment of 120 electronics components
contains 10 defective components. If the control engineer selects 6
of these components at random and test them
a. What is the probability that exactly 3 of those selected are
defective? What is the probability that exactly 4 of those selected
are not defective?
b. What is the probability that at least 3 of those selected are
defective?
c. What is the probability that fewer than 4 selected are not
defective?

Components of a certain type are shipped to a supplier in
batches of ten. Suppose that 79% of all such batches contain no
defective components, 15% contain one defective component, and 6%
contain two defective components. Two components from a batch are
randomly selected and tested. What are the probabilities associated
with 0, 1, and 2 defective components being in the batch under each
of the following conditions?
One of the two tested components is defective.
2 ___________
Show all...

Components of a certain type are shipped to a supplier in
batches of ten. Suppose that 49% of all such batches contain no
defective components, 27% contain one defective component, and 24%
contain two defective components. Two components from a batch are
randomly selected and tested. What are the probabilities associated
with 0, 1, and 2 defective components being in the batch under each
of the following conditions? (Round your answers to four decimal
places.)
(a) Neither tested component is...

The number of times a geyser erupts in one day follows a Poisson
distribution with mean 2.5. On a randomly selected day:
(a) what is the probability that there are no eruptions? (b)
what is the probability of at least 3 eruptions?

The manager of an assembly process wants to determine whether or
not the number of defective articles manufactured depends on the
day of the week the articles are produced. She collected the
following information. Is there sufficient evidence to reject the
hypothesis that the number of defective articles is independent of
the day of the week on which they are produced? Use α =
0.05.
Day of Week
M
Tu
W
Th
F
Nondefective
86
86
95
90
91
Defective...

1. An automobile manufacturer has determined that 33% of all gas
tanks that were installed on its 2015 compact model are defective.
If 16 of these cars are independently sampled, what is the
probability that at least 6 of the sample need new gas tanks?
2. Use the Poisson Distribution Formula to find the indicated
probability: Last winter, the number of potholes that appeared on a
9.0-mile stretch of a particular road followed a Poisson
distribution with a mean of...

The number of traffic accidents in a certain area follows a
Poisson process with a rate of 1.5 per hour between 8:00 A.M. and
5:00 P.M. during the normal working hours in a working day. Compute
the following probabilities.
There will be no traffic accident between 11:30 AM to 12:00
PM.
There will be more than 3 traffic accidents after 3:45
P.M.
There will be in between 15 and 18 traffic accident during the
normal working hours in a working...

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...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 4 minutes ago

asked 5 minutes ago

asked 8 minutes ago

asked 12 minutes ago

asked 16 minutes ago

asked 21 minutes ago

asked 22 minutes ago

asked 38 minutes ago

asked 38 minutes ago

asked 41 minutes ago

asked 49 minutes ago

asked 49 minutes ago