Question

A simple random sample of size n=13 is obtained from a population with μ=67 and σ=16.

(a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities involving the sample mean? Assuming that this condition is true, describe the sampling distribution of x.

(b) Assuming the normal model can be used, determine P(x<70.9).

(c) Assuming the normal model can be used, determine P(x≥68.9).

(a) What must be true regarding the distribution of the population?

A. The population must be normally distributed.

B. The sampling distribution must be assumed to be normal.

C. The population must be normally distributed and the sample size must be large.

D. Since the sample size is large enough, the population distribution does not need to be normal.

(b) P(x<70.9)=__ (Round to four decimal places as needed.)

(c) P(x≥68.9)=__ (Round to four decimal places as needed.)

Answer #1

(a) What must be true regarding the distribution of thepopulation?

A. The population must be normally distributed.

(b) and (c)

A simple random sample of size n=11 is obtained from a
population with μ=68 and σ=17.
(a) What must be true regarding the distribution of the
population in order to use the normal model to compute
probabilities involving the sample mean? Assuming that this
condition is true, describe the sampling distribution of barx.
(b) Assuming the normal model can be used, determine P(bar x
< 71.4).
(c) Assuming the normal model can be used, determine P(bar x
≥ 69.6).

A simple random sample of size n equals =10 is obtained from a
population with μ equals = 62 and σ equals = 18. (a) What must be
true regarding the distribution of the population in order to use
the normal model to compute probabilities involving the sample
mean? Assuming that this condition is true, describe the sampling
distribution of x overbar x. (b) Assuming the normal model can be
used, determine P( x overbar x less than < 65.7)....

Suppose a simple random sample of size n is obtained from a
population whose size is N and whose population proportion with a
specified characteristic is Complete parts (a) through (c) below. =
1000 = 2,000,000 p = 0.25. Click here to view the standard normal
distribution table (page 1).7 Click here to view the standard
normal distribution table (page 2).8 (a) Describe the sampling
distribution of p. A. Approximately normal, μ and p = 0.25 σ p ≈
0.0137...

Suppose a simple random sample of size n=200 is obtained from a
population whose size is N=10,000 and whose population proportion
with a specified characteristic is p=0.6.
Complete parts (a) through
(c) below.
(a) Describe the sampling distribution of
ModifyingAbove p with caretp.
Determine the mean of the sampling distribution of
ModifyingAbove p with caretp.
mu Subscript ModifyingAbove p with caret equals
μp=___
(Round to one decimal place as needed.)
Determine the standard deviation of the sampling distribution
of
sigma...

A simple random sample of size n=40 is obtained from a
population with μ = 50 a n d σ = 4. Does the population
distribution need to be normally distributed for the sampling
distribution of x ¯ to be approximately normally distributed? Why
or why not? What is the mean and standard deviation of the sampling
distribution?

A simple random sample of size
n=81
is obtained from a population with
μ=77
and
σ=27.
(a) Describe the sampling distribution of
x.
(b) What is
P x>80.9?
(c) What is
P x≤69.95?
(d) What is
P 72.8<x<83.9?

Suppose a simple random sample of size nequals36 is obtained
from a population that is skewed right with mu equals 81 and sigma
equals 6.
(a) Describe the sampling distribution of x overbar.
(b) What is Upper P left parenthesis x overbar greater than
82.1 right parenthesis?
(c) What is Upper P left parenthesis x overbar less than or
equals 78.5 right parenthesis?
(d) What is Upper P left parenthesis 79.9 less than x overbar
less than 82.65 right parenthesis?...

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)?

Q4. A simple random sample of size n=180 is obtained from a
population whose size=20,000 and whose population proportion with a
specified characteristic is p=0.45. Determine whether the sampling
distribution has an approximately normal distribution. Show your
work that supports your conclusions.
Q5. Using the values in Q4, calculate the probability of
obtaining x=72 or more individuals with a specified
characteristic.

Suppose a simple random sample of size n=1000 is obtained from a
population whose size is N=1,500,000 and whose population
proportion with a specified characteristic is p=0.55 .
a) What is the probability of obtaining x=580 or more
individuals with the characteristic?
P(x ≥ 580) = (Round to four decimal places as
needed.)
(b) What is the probability of obtaining x=530 or fewer
individuals with the characteristic?
P(x ≤ 530) = (Round to four decimal places as
needed.)

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