Question

approximate p{23<x<31} wherr X us the mean of a random sample
of size 36 with a distribution with mesn u=35 and varience o^2=
16

Answer #1

what is the approximate distribution of the mean of a random sample
size 36 frim a population whose mean and standard deviation are 20
and 12 respectively? why?

Suppose a random sample of n=36 measurements is selected from a
population with mean u=256 and variance o^2=144.
a. Describe the sampling distribution of the sample mean x bar.
(Hint: describe the shape, calculate the mean and the standard
deviation of the sampling distribution of x bar.
b. What is the probability that the sample mean is greater than
261?

5-1. Consider a random sample of size 36 from a normal
distribution (population) with a mean of 10 and a standard
deviation of 6. Which of the following statement is false?
(a) The mean of X¯ is 10. (b) The standard deviation of X¯ is 1.
(c) X¯ approximately follows a normal distribution. (d) There is an
incorrect statement in the alternatives above.
5-2. Let X1, . . . , X36 be a random sample from Bin(36, 0.5).
Which of...

Suppose a simple random sample of size n=36 is obtained from a
population with μ= 89 and σ= 12. Find the mean and standard
deviation of the sampling distribution of X.
a) What is P (x > 91.4)?
b) What is P (x ≤ 84.8)?
c) What is P(86< x<93.3)?

Consider a random sample from a Weibull distribution,
Xi~WEI(1,2). Find approximate values a and b such that
for n=35:
P(a<X<b)=0.95, where X=X18:35 is the sample
median.
Note: X is the MEDIAN, NOT the mean.

Suppose x has a mound-shaped distribution. A random sample of
size 16 has sample mean 10 and sample standard deviation 2.
(b) Find a 90% confidence interval for μ
(c) Interpretation Explain the meaning of the confidence
interval you computed.

A sample mean, sample size, and population standard deviation
are provided below. Use the one-mean z-test to perform the
required hypothesis test at the 55% significance level.
x=35, n=34, o=7, H0: u=37, Ha: u<37

simple random sample of size n is drawn. The
sample mean,
x overbarx,
is found to be
19.1
and the sample standard deviation, s, is found
to be
4.14
(a) Construct a
95%
confidence interval about
muμ
if the sample size, n, is
35.

Let ? ̅ and ?2 be the mean and variance of a random sample of
size 16 from a normal distribution N(4, 128). Find (a) ?(5 < ? ̅
< 8) (b) ?(200 < ?2 < 262.4)

Suppose that a random sample of size 64 is to be selected from a
population with mean 40 and standard deviation 5.
(a) What are the mean and standard deviation of the sampling
distribution?
μx =
σx =
(b) What is the approximate probability that x will be
within 0.4 of the population mean μ? (Round your answer to
four decimal places.)
P =
(c) What is the approximate probability that x will differ
from μ by more than 0.8?...

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