Question

A random sample is selected from a population with mean μ = 100 and standard deviation σ = 10.

Determine the mean and standard deviation of the x sampling distribution for each of the following sample sizes. (Round the answers to three decimal places.)

(a) n = 8 μ = σ =

(b) n = 14 μ = σ =

(c) n = 34 μ = σ =

(d) n = 55 μ = σ =

(f) n = 110 μ = σ =

(e) n = 440 μ = σ =

A random sample is selected from a population with mean
*μ* = 101 and standard deviation *σ* = 10. For which
of the sample sizes would it be reasonable to think that the
*x* sampling distribution is approximately normal in shape?
(Select all that apply.)

*n* = 13

*n* = 16

*n* = 41

*n* = 60

*n* = 120

*n* = 480

An airplane with room for 100 passengers has a total baggage limit
of 6000 lb. Suppose that the total weight of the baggage checked by
an individual passenger is a random variable *x* with a mean
value of 51 lb and a standard deviation of 23 lb. If 100 passengers
will board a flight, what is the approximate probability that the
total weight of their baggage will exceed the limit? (Hint: With
*n* = 100, the total weight exceeds the limit when the
average weight *x* exceeds 6000/100.) (Round your answer to
four decimal places.)

A random sample is to be selected from a population that has a
proportion of successes *p* = 0.69. Determine the mean and
standard deviation of the sampling distribution of *p̂* for
each of the following sample sizes. (Round your standard deviations
to four decimal places.)

(a) *n* = 30

mean | ||

standard deviation |

(b) *n* = 40

mean | ||

standard deviation |

(c) *n* = 50

mean | ||

standard deviation |

(d) *n* = 70

mean | ||

standard deviation |

(e) *n* = 120

mean | ||

standard deviation |

(f) *n* = 220

mean | ||

standard deviation |

An article reported that in a large study carried out in the
state of New York, approximately 30% of the study subjects lived
within 1 mile of a hazardous waste site. Let *p* denote the
proportion of all New York residents who live within 1 mile of such
a site, and suppose that *p* = 0.3.

(a) Would *p̂* based on a random sample of only 10
residents have approximately a normal distribution? Explain why or
why not.

Yes, because *n**p* < 10 and
*n*(1 − *p*) < 10.Yes,
because *n**p* > 10 and *n*(1 −
*p*) > 10. No, because
*np* < 10.No, because *np* > 10.

(b) What are the mean value and standard deviation of *p̂*
based on a random sample of size 420? (Round your standard
deviation to four decimal places.)

mean | ||

standard deviation |

(c) When *n* = 420, what is *P*(0.25 ≤ *p̂* ≤
0.35)?

(d) Is the probability calculated in Part (c) larger or smaller
than would be the case if *n* = 520? Answer without actually
calculating this probability.

The probability from Part (c) is smaller because as *n*
increases, the standard deviation of *p̂* decreases.The
probability from Part (c) is larger because as *n*
increases, the standard deviation of *p̂*
increases. The probability from Part
(c) is larger because as *n* increases, the standard
deviation of *p̂* decreases.The probability from Part (c) is
smaller because as *n* increases, the standard deviation of
*p̂* increases.

Answer #1

Part a)

Part b)

Part c)

Part d)

Part e)

Part f)

A random sample is selected from a population with mean
μ = 102 and standard deviation σ = 10. Determine
the mean and standard deviation of the x sampling
distribution for each of the following sample sizes. (Round the
answers to three decimal places.)
(a) n = 12
μ =
σ =
(b) n = 13
μ =
σ =
(c) n = 37
μ =
σ =
(d) n = 70
μ =
σ =
(f) n = 140...

A random sample is to be selected from a population that has a
proportion of successes p = 0.68. Determine the mean and
standard deviation of the sampling distribution of p̂ for
each of the following sample sizes. (Round your standard deviations
to four decimal places.)
(a) n = 10
standard deviation
(b) n = 20
standard deviation
(c) n = 30
standard deviation
(d) n = 50
standard deviation
(e) n = 100
standard deviation...

A random sample of size n = 49 is selected from a population
with mean μ = 54 and standard deviation σ = 14. What will be the
mean and standard deviation of the sampling distribution of x?

A random sample is drawn from a population with mean μ = 72 and
standard deviation σ = 6.0. [You may find it useful to reference
the z table.]
a. Is the sampling distribution of the sample mean with n = 17
and n = 45 normally distributed?
Yes, both the sample means will have a normal distribution.
No, both the sample means will not have a normal
distribution.
No, only the sample mean with n = 17 will have...

A random sample is drawn from a population with mean μ
= 52 and standard deviation σ = 4.3.
a. Is the sampling distribution of the sample
mean with n = 13 and n = 39 normally
distributed?
Yes, both the sample means will have a normal distribution.
No, both the sample means will not have a normal
distribution.
No, only the sample mean with n = 13 will have a normal
distribution.
No, only the sample mean with n...

A random sample is to be selected from a population that has a
proportion of successes p = 0.69. Determine the mean and
standard deviation of the sampling distribution of p̂ for
each of the following sample sizes. (Round your standard deviations
to four decimal places.)
(a) n = 30
mean
standard deviation
(b) n = 40
mean
standard deviation
(c) n = 50
mean
standard deviation
(d) n = 70
mean
standard deviation
(e) n =...

A random sample is drawn from a population with mean μ
= 53 and standard deviation σ = 4.4. [You may find
it useful to reference the z table.]
a. Is the sampling distribution of the sample
mean with n = 13 and n = 38 normally
distributed?
Yes, both the sample means will have a normal distribution.
No, both the sample means will not have a normal
distribution.
No, only the sample mean with n = 13 will have...

Given the population mean, μ = 45, and the population standard
deviation, σ = 15 with a sample size of, n = 100.n = 100. Determine
P ( x ¯ ≤ 42 ). To do this problem first determine the sampling
mean and the sampling standard deviation in order to convert to a
z-score. Round your answer to 4 decimals.

A random sample is drawn from a normally distributed population
with mean μ = 25 and standard deviation σ =
1.5.
a. Are the sampling distributions of the sample
mean with n = 33 and n = 66 normally
distributed?
Yes, both the sample means will have a normal distribution.
No, both the sample means will not have a normal
distribution.
No, only the sample mean with n = 33 will have a normal
distribution.
No, only the sample mean...

1. A sampling distribution of the mean has a
mean μ X̄ =45 μ X̄ =45 and a
standard error σ X̄ =7 σ X̄ =7
based on a random sample of n=15.n=15.
a. What is the population mean?
b. What is the population standard
deviation?
Round to two decimal places if necessary
2. If it is appropriate to do so, use the normal approximation
to the p^ p^ -distribution to calculate the
indicated probability:
Standard Normal Distribution Table
n=80,p=0.715n=80,p=0.715
P( p̂ > 0.75)P( p̂ > 0.75) =
Enter 0...

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