Question

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?

Answer #1

This distribution will be approximately normal. We know this
from the **central limit theorem** which states that
*the distribution of the sampling means of any
distribution is approximately normal, if the sample size is
sufficiently large (greater than 30)*.

In our case, the sample size is greater than 30. Thus, the distribution will be normal.

The mean of such a distribution is equal to the population mean, and the standard deviation is equal to the population mean divided by the square root of the sample size.

Thus, new distribution mean= old distribution mean= 20

Thus, new distribution standard deviation= old distribution standard deviation= 12/sqrt(36)

= 12/6= 2

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...

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

a simple random sample of size 36 is taken from a normal
population with mean 20 and standard deivation of 15. What is the
probability the sample,neab,xbar based on these 36 observations
will be within 4 units of the population mean. round to the
hundreths placee

a simple random sample of size 36 is taken from a normal
population with mean 20 and standard deivation of 15. What is the
probability the sample,neab,xbar based on these 36 observations
will be within 4 units of the population mean. round to the
hundreths place

1.
Suppose that a random sample of size 36 is to be selected from a
population with mean 49 and standard deviation 9. What is the
approximate probability that will be within 0.5 of the
population mean?
a.
0.5222
b.
0.0443
c.
0.2611
d.
0.4611
e.
0.7389
2.
Suppose that x is normally distributed with a mean of 60 and a
standard deviation of 9. What is P(x 68.73)?
a.
0.834
b.
0.166
c.
0.157
d.
0.334
e.
0.170

A random sample of size 64 is taken from a population with mean
µ = 17 and standard deviation σ = 16. What are the expected value
and the standard deviation for the sampling distribution of the
sample mean?
17 and 2, respectively.
17 and 64, respectively.
17 and 16, respectively.
17 and 1, respectively.

A random sample of size 64 is taken from a population with mean
µ = 17 and standard deviation σ = 16. What are the expected value
and the standard deviation for the sampling distribution of the
sample mean?
17 and 2, respectively.
17 and 64, respectively.
17 and 16, respectively.
17 and 1, respectively.

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)?

Suppose that a random sample of size 64 is to be selected from a
population with mean 40 and standard deviation 5.
(a) What is the mean of the xbar sampling distribution? 40 What
is the standard deviation of the xbar sampling distribution?
.625
(b) What is the approximate probability that xbar will be within
0.5 of the population mean μ ?
(c) What is the approximate probability that xbar will differ
from μ by more than 0.7?

1. A sample size of 49 drawn from a population with a mean of 36
and a standard deviation of 15 for the size of an English class.
What is the probability the class will have greater than 40
a. .9693
b. .4693
c. .0808
d. .0307
2. A sample size of 49 drawn from a population with a mean of 36
and a standard deviation of 15 for the size of an English class.
What is the probability the...

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