Question
In: Statistics and Probability
the following questions are either true or false answers 1. The Central Limit Theorem allows one...
the following questions are either true or false answers
1. The Central Limit Theorem allows one to use the Normal
Distribution for both normally and non-normally distributed
populations.
2. A random sample of 25 observations yields a mean of 106 and
a standard deviation of 12. Find the probability that the sample
mean exceeds 110. The probability of exceeding 110 is 0.9525.
3. Suppose the average time spent driving for drivers age
20-to-24 is 25 minutes and you randomly select 50 drivers. What is
the probability that the mean time they spend driving each day is
between 24.7 and 25.5 minutes, assuming that the standard deviation
is 1.5 minutes?
P(24.7<X<25.5) =0.9116
4. An electrical firm manufactures a certain type of light
bulb that has a mean life of 1,800 hours and a standard
deviation of 200 hours. Find the probability that a random
sample of 100 bulbs will have an average life of more than 1,825
hours.
P(X>1,825) =0.1056
5. A manufacturing company receives a shipment of ball
bearings each month from a supplier. The inspector applies the
following rule in deciding whether or not to accept or reject each
shipment: If the mean diameter of the sample is between 0.245 and
0.255 the shipment is accepted otherwise the shipment is rejected.
A random sample of 36 bearings is selected and measured. What is
the probability of accepting the shipment that has a mean diameter
of 0.240 inches and a standard deviation of 0.015 inches? The
probability of accepting the shipment is 0.0228.
Solutions
orchestra answered 2 years agoRelated Solutions
1. True or False: The central limit theorem justifies the common assumption that the distribution of...
1. True or False: The central limit theorem justifies the common
assumption that the distribution of a
product’s parameters is normal.
2. True or false: An X bar chart with points falling above the
upper control limit is in control.
3.True or False: One or more points that fall outside control
limits indicates that a process is NOT capable
4. One-third of the units produced by a particular process step
do not meet customer-specific tolerances.
Which of the following statements,...
True or False. In order to use results from the Central Limit Theorem for calculating that...
True or False.
In order to use results from the Central Limit Theorem for
calculating that the sample mean is greater than some number, the
population you are sampling from must have a normal
distribution.
If a variable has a binomial distribution with the probability
of success equal to 0.82, then the distribution is skewed to the
left.
For calculating the probability that a sample mean is greater
than some given value, in solving this problem, one of the first...
The central limit theorem is an important concept in research. It allows several key assumptions to...
The central limit theorem is an important concept in research.
It allows several key assumptions to be made, and facilitates
several key practices.
Implications
For this discussion, you will reflect
on the application of the central limit theorem to research.
Develop the main response in which you address the following
Summarize the implications of the central limit theorem.
Identify what you believe to be the most important application
of it.
Explain your position, providing examples where possible.
Give as much...
This week we’ve introduced the central limit theorem. According to the central limit theorem, for all...
This week we’ve introduced the central limit theorem. According to
the central limit theorem, for all samples of the same size n with
n>30, the sampling distribution of x can be approximated by a
normal distribution.
In your initial post
use your own words to explain what this theorem means. Then provide
a quick example to explain how this theorem might apply in real
life. At last, please share with us your thoughts about why this
theorem is important.
There are 4 conditions that must be true in order to use the Central Limit theorem.
There are 4 conditions that must be true in order to use
the Central Limit theorem. 1) We must have a simple random sample
(SRS); 2) the sample size must be less than 10% of the population;
3) the observations must be independent; and 4) the sample size
must be large enough so that both np > 10 and n(1 - p) >10,
in which the true proportion (or probability) possessing the
attribute of interest is p. Then the Central...
There are 4 conditions that must be true in order to use the Central Limit theorem.
Part 3: The Central Limit Theorem for a Sample
ProportionThere are 4 conditions that must be true in order to use
the Central Limit theorem. 1) We must have a simple random sample
(SRS); 2) the sample size must be less than 10% of the population;
3) the observations must be independent; and 4) the sample size
must be large enough so that both np > 10 and n(1 - p) >10,
in which the true proportion (or probability) possessing...
There are 4 conditions that must be true in order to use the Central Limit theorem....
There are 4 conditions that must be true in order to use
the Central Limit theorem. 1) We must have a simple random sample
(SRS); 2) the sample size must be less than 10% of the population;
3) the observations must be independent; and 4) the sample size
must be large enough so that both np > 10 and n(1 - p) >10,
in which the true proportion (or probability) possessing the
attribute of interest is p. Then the Central...
Which of the following are valid limitation of the central limit theorem? Select one or more...
Which of the following are valid limitation of the central limit
theorem?
Select one or more answers:
1) The random variables must have finite variance
2) The random variables must have finite mean
3) The random variables under sample average must be normal
4)The random variables must be under sample average
5) The random variables under sample average must be i.i.d
Question5. Please answer the following questions as either "TRUE" or "FALSE" (Write out either “True” or...
Question5. Please answer the following questions as either
"TRUE" or "FALSE" (Write out either “True” or “False”)
A. A normal distribution is characterized by its mean and its
degrees of freedom. ______________
B. A paired t-test is considered a nonparametric test.
______________
C. A 93% confidence interval for µ is that numerical interval
constructed to contain 93% of the values of µ. ____________
D. A 94% confidence interval for a mean is narrower than a 93%
confidence interval. ______________
E....
the following questions are either true or false. 1. Suppose that x is a normally distributed...
the following questions are either true or false.
1. Suppose that x is a normally distributed random variable, with a
mean of 10 and a cariance of 4. then probability that x lies
between 11.0 and 13.6 is 0.02726
2. Find E(X)= mean id X is a normally distributed random
vaeiqvle with standard deviation 1 and if X is a normally
distributed random variable with standard deviation 1 and with
P(x>5)=0.6915 mean= E(X) =5.50
3. Find P(-0.47<Z<0.94)=0.5666
4. In a...
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