Question

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).

Answer #1

The distribution of population must be normal and using central limiting theorem the distribution of is normal with mean and standard deviation

We define the standard random variable Z as

b) Using Normal table we have

c)

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)....

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...

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 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)?

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?

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=39 is obtained from a
population with μ=6666 and σ=14.
P(x overbar < 69.2) =
P(x overbear great than or equal to 67.8) =

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.

A simple random sample size of n=800 is obtained from a
population whose size is N=10,000,000 and whose population
proportion with a specified characteristic is p=.32.
a)describe the sampling distribution
b) What is the probability of obtaining x=350 or more
individuals with the characteristic?

Suppose a simple random sample of size
nequals=36
is obtained from a population with
μ=81
and
sigma equals 6.
(a) Describe the sampling distribution of
x overbarx.
(b) What is
Upper P left parenthesis x overbar greater than 82.55 right
parenthesisP x>82.55?
(c) What is
Upper P left parenthesis x overbar less than or equals 78.85
right parenthesisP x≤78.85?
(d) What is
Upper P left parenthesis 79.9 less than x overbar less than
82.85 right parenthesisP 79.9<x<82.85?

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