Question

Suppose that you are interested in estimating the average number
of miles per gallon of gasoline your car can get. You calculate the
miles per gallon for each of the next ten times you fill the tank.
Suppose that in truth, the values for your car are bell-shaped,
with a mean of 25 miles per gallon and a standard deviation of 1.
Find the possible sample means you are likely to get based on your
sample of ten observations. Consider the intervals into which 68%,
95%, and almost all of the potential sample means will fall, using
the Empirical Rule. (Round all answers to the nearest
thousandth.)

About 68% of possible sample means will be in the range
between and .

About 95% of possible sample means will be in the range
between and .

About 99.7% of possible sample means will be in the range
between and .

The weights of men in a particular age group have mean
*μ* = 154 pounds and standard deviation *σ* = 30
pounds.

(a) For randomly selected samples of *n* = 9 men, what is
the standard deviation, *s.d.*, of the sampling distribution
of possible sample means?

* s*.

=

(b) For randomly selected samples of *n* = 36 men, what is
the standard deviation, s.d., of the sampling distribution of
possible sample means?

* s*.

=

A randomly selected sample of *n* = 85 individuals over
65 years old takes a test of memorization skills. The sample mean
is *x* = 53, and the standard deviation is *s* = 6.8.
Give the numerical value of the standard error of the mean,
*s.e.* (Round your answer to two decimal places.)

* s*.

Suppose that you are interested in estimating the average number of
miles per gallon of gasoline your car can get. You calculate the
miles per gallon for each of the next ten times you fill the tank.
Suppose that in truth, the values for your car are bell-shaped,
with a mean of 25 miles per gallon and a standard deviation of 1.
Find the possible sample means you are likely to get based on your
sample of ten observations. Consider the intervals into which 68%,
95%, and almost all of the potential sample means will fall, using
the Empirical Rule. (Round all answers to the nearest
thousandth.)

About 68% of possible sample means will be in the range
between and .

About 95% of possible sample means will be in the range between
and. .

About 99.7% of possible sample means will be in the range
between and .

Suppose the population of IQ scores in the town or city where
you live is bell-shaped, with a mean of 109 and a standard
deviation of 17. Describe the distribution of possible sample means
that would result from random samples of 100 IQ scores.

The distribution will be approximately a normal curve with
mean and standard deviation .

Answer #1

1)

about 68% of observation of data lie within 1 std dev away from
mean

about 95% of observation of data lie within 2 std dev away from
mean

about 99.7% of observation of data lie within 3 std dev away from
mean

µ=25

σx=σ/√n = 1/√10 = 0.316

**About 68% of possible sample means will be in the range
between X̄ ± 1 * s = ( 24.684 ,
25.316 )
About 95% of possible sample means will be in the range
between X̄ ± 2 * s = ( 24.368
25.632 )
About 99.7% of possible sample means will be in the range
between and .X̄ ± 3 * s = (
24.051 25.949
)**

=====================

2)

a) σx = std error = σ/√n= 30/√9 = 10

b) σx = std error = σ/√n= 30/√36 = 5

c) s.e.(x) =std error = σ/√n= 6.8/√85 = 0.74

The miles-per-gallon obtained by the 1995 model Z cars is
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miles-per-gallon? b. What is the probability that a car will get
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