Question

For each of the following scenarios, state whether the normal distribution may be used and justify your answer. If the normal distribution can't be used, state which distribution should be used instead.

a. A random sample of size 15 is taken from a normal population
with standard deviation 5. Find the probability that the sample
**mean** is greater than 28.

b. A random sample of size 15 is taken from a normal population
with standard deviation 5. Find the probability that the sample
**variance** is greater than 28.

c. A random sample of size **125** is taken from an
approximately normal population. Find the probability that the
sample mean is greater than 28.

d. A random sample of size **15** is taken from an
approximately normal population. Find the probability that the
sample mean is greater than 28

Answer #1

Determine whether the
z
-test or the
t
-test should be performed, or whether a statistician should be
consulted.
Part 1 of 3
A simple random sample of size
23
has mean
x
=
41.8
. The population standard deviation is σ
=
3.72
. The population is normally distributed. Can you conclude that
the population mean differs from
40
?
The population standard deviation
▼(Choose one) known. The sample size
n
▼(Choose one) greater than
30
. The population...

In which of the following scenarios can we assume a Normal
distribution for the sample mean? a. Sample of size 2 comes from a
population with normal distribution (known variance) b. Sample of
size 10 comes from a population with normal distribution (unknown
variance) c. Sample of size 300 comes from a population with some
unknown distribution d. Sample of size 15 comes from a population
with some unknown distribution

The distribution of the commute times for the employees at a
large company has mean 22.4 minutes and standard deviation 6.8
minutes. A random sample of n employees will be selected and their
commute times will be recorded. What is true about the sampling
distribution of the sample mean as n increases from 2 to 10 ? The
mean increases, and the variance increases. A The mean increases,
and the variance decreases.
B The mean does not change, and the...

Which of the following is NOT true regarding the sampling
distribution of the mean (Sample mean X-bar) for a large sample
size (sample size is greater than 36)? A. It has the same mean as
the population. B. It has a smaller standard deviation than the
population standard deviation. C. Approximately it follows a normal
distribution. D. It has the same distribution as the
population.

Can a normal approximation be used for a sampling distribution
of sample means from a population with μ=43 and σ=8, when
n=36?
Answer
TablesKeypad
Yes, because the mean is greater than 30.
No, because the sample size is more than 30.
Yes, because the sample size is at least 30.
No, because the standard deviation is too small.

Question: Eleven:
(a) In a sample of 16 observations from a normal distribution
with mean 150 and variance of 256. Find the following
probabilities
i. Ρ ( Χ ≤160) ii. Ρ ( Χ ≥142)
(b) The age of employees in a company follows a normal
distribution with its mean and variance as 40 years and 121 years,
respectively. If a random sample of 36 employees is taken from a
normal population of size 1000, what is the probability that the...

Suppose that the random sample is taken from a normal
distribution N(8,9), and the random sample is between 1 to 25.
Find the distribution of the sample mean.
Find probability that the sample mean is less than or equal to
8.8 and the sample variance is less than or equal to 12.45, where
the probabilities are independent.
Find probability that the sample mean is less than 8+(.5829)S,
where S is the sample standard deviation.

A normally distributed population has a mean of
560
and a standard deviation of
60
.
a. Determine the probability that a random sample of size
25
selected from this population will have a sample mean less
than
519
.
b. Determine the probability that a random sample of size
16
selected from the population will have a sample mean greater
than or equal to
589
Although either technology or the standard normal distribution
table could be used to find...

The lifetime of a tire can be represented by a
normal distribution with an average of 35,000 kilometers and a
standard deviation of 4,000 kilometers.
Find the probability that the time of a tire is more than
30,000 kilometers.
Find the value of K such that the probability that the life
time of a tire is less than K is 0.95.
A sample of 80,000 was taken from these tires. Approximately
how many have a life time greater than 38,000...

A population of values has a normal distribution with μ = 8.2
and σ = 30.2 . You intend to draw a random sample of size n = 28 .
Find the probability that a single randomly selected value is
greater than -0.9. P(X > -0.9) = Find the probability that a
sample of size n = 28 is randomly selected with a mean greater than
-0.9. P(M > -0.9) = Enter your answers as numbers accurate to 4
decimal...

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