Question

Assume the population of fully loaded delux SUVs has a mean cost of $62,000 with a standard deviation of $5,100. We dont know the exact distribution of the costs, just the population mean and standard deviation.

A. We plan to take a ranodm sample of fully loaded deluxe SUVs and calculate the mean cost for analysis. Approximately, how big should our sample be so we dont care about the exact distribution of cost.

We take a random sample of 100 loaded deluxe SUVs and caluclate the mean cost.

B. What is the standard error of the mean

C. State the probability distribution (sampling distribution) of x bar

D. What is the probability x bar will fall between $61,000-$62,500?

E. What is the probability x bar will fall within $1,500 of the mean?

F. What will happen to the sampling distribution of x bar if we increase our sample size

G. What values of x bar would indicate we have an outlier?

Answer #1

a)from central limit theorum minimum sample size required is 30 for sample mean to be approximately normal

b)

standard error of the mean =std deviation/sqrt(n)=5100/sqrt(100)=510

c)

sampling distribution of mean(xbar) is approximately normal with estimaed mean =62000 and std error of mean =510

d)

for normal distribution z score =(X-μ)/σx | |

here mean= μ= | 62000 |

std deviation =σ= | 5100.000 |

sample size =n= | 100 |

std error=σ_{x̅}=σ/√n= |
510.0000 |

probability = | P(61000<X<62500) | = | P(-1.96<Z<0.98)= | 0.8365-0.025= | 0.8115 |

e)

probability x bar will fall within $1,500 of the mean:

probability = | P(60500<X<63500) | = | P(-2.94<Z<2.94)= | 0.9984-0.0016= | 0.9968 |

f)

as we increase our sample size standard error of mean decreases .

g)

as 3 std deviation away values are outlier ;

therefore outlier fences =mean -/+3*std error=6200-/+3*5100=60470 to 63530

hence values below 60470 and above 63530 should be considered outlier.

A certain test has a population mean (mu) of 285 with a
population standard deviation (sigma) or 125. You take an SRS of
size 400 find that the sample mean (x-bar) is 288.
The sampling distribution of x-bar is approximately Normal with
mean:
The sampling distribution of x-bar is approximately Normal with
standard deviation:
Based on this sample, a 90% confidence interval for mu is:
Based on this sample, a 95% confidence interval for mu is:
Based on this sample,...

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?

Weights of a certain model of fully loaded gravel trucks follow
a normal distribution with mean µ = 8.6 tons and standard deviation
ơ = 0.5 tons. What is the probability that a fully loaded truck of
this model is:
a.) More than 7 tons?
b.) Less than 9.6 tons?
c.) Between 8.3 and 8.9 tons?

Assume for a moment that we have a population distribution that
is negatively skewed. Which probability distribution becomes normal
as the size of the sample increases?
population distribution
sample distribution
sampling distribution
None of the above
The standard error of the mean refers to the standard deviation
of the...
normal distribution
population
sample
sampling distribution
None of the above
Which type of error can be quantitatively measured:
sampling error
non-sampling error
both
neither
The purpose of statistical inference is to...

The mean cost for college textbooks per semester is $636 with a
standard deviation of $117. If all possible random samples of size
49 are taken from this population, determine the following:
a) name of the Sampling Distribution?
b) mean and standard error of the sampling distribution of the
mean (use the correct name and symbol for each)?
c) percent of sample means that are less than $600?
d) probability that sample means fall between $500 and $800?
e) Below...

The population has mean μ=29 and standard deviation σ=9.
This distribution is shown with the black dotted line.
We are asked for the mean and standard deviation of the
sampling distribution for a sample of size 34. The Central Limit
Theorem states that the sample mean of a sample of size n is
normally distributed with mean μx¯=μ and σx¯=σn√.
In our case, we have μ=29, σ=9, and n=34. So,
μx¯=29
and
σx¯=934‾‾‾√=1.5
This distribution is shown with the red...

If the sampled population has a mean 48 and standard deviation
18, then the mean and the standard deviation for the sampling
distribution of (X-bar) for n = 9 are:
A. 48 and 18
B. 48 and 9
C. 16 and 6
D. 48 and 6
E. 48 and 2

If the sampled population has a mean 48 and standard deviation
18, then the mean and the standard deviation for the sampling
distribution of (X-bar) for n = 9 are:
A. 48 and 18
B. 48 and 9
C. 16 and 6
D. 48 and 6
E. 48 and 2

a. If X is a normal random variable with mean 10, and if the
probability that X is less than 11.54 is .72 then what is the
standard deviation of X?
1.75
3.50
4.20
12.25
b. If the standard deviation of a population is 36 and we take a
sample of size 9, then the standard error (the standard deviation
of the sample mean) is
12.00
3.00
108.00
4.00
c. According to the empirical rule, in a normal distribution
about...

A population has a mean of 75 and a standard deviation of 32.
Suppose a random sample size of 80 will be taken.
1. What are the expected value and the standard deviation of the
sample mean x ̅?
2. Describe the probability distribution to x ̅. Draw a graph of
this probability distribution of x ̅ with its mean and standard
deviation.
3. What is the probability that the sample mean is greater than
85? What is the probability...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 7 minutes ago

asked 14 minutes ago

asked 16 minutes ago

asked 26 minutes ago

asked 43 minutes ago

asked 50 minutes ago

asked 58 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago