Question

an electronics company finishes a production run of 5000 tablet computers, which includes 900 defective units. To test this batch for defects, a random sample of 100 tablets is drawn (without replacement) and tested. Let X be the random variable that counts the number of defective units among the sample.

a. find the expected (mean) value, variance, and standard deviation of X

b. the probability distribution of X can be approximated with a binomial distribution. Why?

c. Use the binomial approximation to find the approximate probability that the sample includes exactly 15 defective units.

d. Find the approximate probability that X is within 1 standard deviation of its mean value

Answer #1

Question 1: Suppose that of 6,000 electrical fuses, 5% are
defective. Also, suppose that a random sample of 10 fuses is
selected and consider the random variable X representing the number
of defective fuses in the sample. (a) Explain why a binomial
distribution is appropriate. (b) What is the probability that at
least one of the fuses is defective? (c) What is the probability
that fewer than 3 fuses are defective?
Question 2: Refer to the setup in Question 1....

A company operates an assembly line. The company believes that
there is a 3% probability that any given item produced on the line
will contain a defect. If 100 items are pulled at random from the
line, what is the probability there will be exactly 4 defective
items? ____
If 100 items are pulled at random from the line, what is the
probability there will be 9 or more defective items? _______
If X = the number of defectives in...

1. For a binomial distribution, if the probability of success is
0.621 on the first trial, what is the probability of success on the
second trial?
2.A company purchases shipments of machine components and uses
this acceptance sampling plan:
Randomly select and test 32 components and accept the whole batch
if there are fewer than 5 defectives.If a
particular shipment of thousands of components actually has a 5.5%
rate of defects, what is the probability that this whole shipment
will...

True or False:
10. The probability of an event is a value which must be greater
than 0 and less than 1.
11. If events A and B are mutually exclusive, then P(A|B) is always
equal to zero.
12. Mutually exclusive events cannot be independent.
13. A classical probability measure is a probability assessment
that is based on relative frequency.
14. The probability of an event is the product of the probabilities
of the sample space outcomes that correspond to...

One way of checking the effect of undercoverage, nonresponse,
and other sources of error in a sample survey is to compare the
sample with known facts about the population. About 14% of American
adults are black. The numbers X of blacks in a random
sample of 1700 adults should therefore vary with the binomial
(n = 1700, p = 0.14) distribution.
(a) What are the mean and standard deviation of X?
(Round your standard deviation to three decimal places.)
mean...

1.A weekend TV game show called rolling a dice is running each
week. For each roll, if the dice shows an odd number the
participate earns 5 dollars and otherwise, he gets nothing. Each
participate can roll the dice 20 times. Let X denote the number
times the dice shows an odd number.
a) (2 mark) Calculate the average earning of a
participate.
b) Calculate the probability that ? ⩽ 2 (show your
final answer correct to four decimal places)....

A. The personnel office at a large electronics firm regularly
schedules job interviews and maintains records of the interviews.
From the past records, they have found that the length of a first
interview is normally distributed, with mean μ = 38 minutes and
standard deviation σ = 4 minutes. (Round your answers to four
decimal places.)
(i) What is the probability that a first interview will last 40
minutes or longer?____________________
(ii) Ten first interviews are usually scheduled per day....

*Answer all questions using R-Script*
Question 1
Using the built in CO2 data frame, which contains data from an
experiment on the cold tolerance of Echinochloa crus-galli; find
the following.
a) Assign the uptake column in the
dataframe to an object called "x"
b) Calculate the range of x
c) Calculate the 28th percentile of
x
d) Calculate the sample median of
x
e) Calculate the sample mean of x and
assign it to an object called "xbar"
f) Calculate...

BridgeRock is a major manufacturer of tires in the U.S.. The
company had five manufacturing facilities where tires were made and
another 20 facilities for various components and materials used in
tires. Each manufacturing facility produced 10,000 tires every
hour. Quality had always been emphasized at BridgeRock, but lately
quality was a bigger issue because of recent fatal accidents
involving tires made by other manufacturers due to tread
separation. All tire manufacturers were under pressure to ensure
problems did not...

2) A market research company wishes to find out which of two
internet search engines the
population of students at a university prefers to use: Google or
MSN Search. A random sample
of students is selected, and each one is asked to search for a
certain subject using Google and
then MSN, or vice versa. The order of the two searches was
determined at random. They then
indicate which internet search engine they prefer. What type of
study is this?...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 1 minute ago

asked 18 minutes ago

asked 18 minutes ago

asked 23 minutes ago

asked 45 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago