Question

Ralph’s Bookstores have indicated that the annual gross revenue for their stores is µ=$250,000 with a standard deviation of σ=$50,000.

**Blank #1 (a):** Find the probability that the
annual gross revenue is more than $260,000. Report your answer to 4
decimal places. If this is a probability that cannot be determined,
then state unknown as your answer.

**Blank #2 (b)**: A random sample of 25 stores is
chosen. Find the probability that the mean annual gross revenue is
more than $260,000. Report your answer to 4 decimal places. If this
is a probability that cannot be determined, then state unknown as
your answer.

**Blank #3 (c):** A random sample of 40 stores is
chosen. Find the probability that the mean annual gross revenue is
more than $260,000. Report your answer to 4 decimal places. If this
is a probability that cannot be determined, then state unknown as
your answer.

**Blank #4 (d):** If the sample size were to
increase, how would the probability compare to what you found in
part (c)? (smaller, larger, equal).

The number of Girl Scout cookies sold by each of the girl scouts in Central City has a distribution that is approximately normal with µ = 100 boxes and a standard deviation σ = 40 boxes.

**2: Blank #1 (a):** Find the probability that a
girl scout chosen at random sold between 80 and 120 boxes. Report
your answer to 4 decimal places. If this is a probability that
cannot be determined, then state unknown as your answer.

**Blank #2 (b):** Find the probability that the
mean number of cookies sold by a random sample of 36 scouts is
between 80 and 120 boxes. Report your answer to 4 decimal places.
If this is a probability that cannot be determined, then state
unknown as your answer.

Please explain how to do it clearly.

Answer #1

A bookstore chain claims that the annual gross revenue for all
of their stores has a mean revenue of 350000 with a standard
deviation of 82000, A random sample of 121 stores is selected.
A. Find the mean and the standard deviation for this sampling
distribution
B. Find the probability that the mean annual gross revenue is
between 350,000 and 360,000

The owner of a movie theater company would like to predict
weekly gross revenue as a function of advertising expenditures.
Historical data for a sample of eight weeks follow.
Weekly
Gross
Revenue
($1,000s)
Television
Advertising
($1,000s)
Newspaper
Advertising
($1,000s)
96
5
1.5
91
2
2
95
4
1.5
93
2.5
2.5
95
3
3.3
94
3.5
2.3
94
2.5
4.1
94
3
2.5
(a)Use α = 0.01 to test the hypotheses
H0:
β1 = β2 = 0
Ha:
β1 and/or...

The owner of a movie theater company would like to predict
weekly gross revenue as a function of advertising expenditures.
Historical data for a sample of eight weeks follow.
Weekly
Gross
Revenue
($1,000s)
Television
Advertising
($1,000s)
Newspaper
Advertising
($1,000s)
96
5
1.5
90
2
2
95
4
1.5
93
2.5
2.5
95
3
3.3
94
3.5
2.2
94
2.5
4.1
94
3
2.5
(a)
Use α = 0.01 to test the hypotheses
H0:
β1 = β2 = 0
Ha:
β1...

1. The owner of a movie theater company would like to predict
weekly gross revenue as a function of advertising expenditures.
Historical data for a sample of eight weeks follow.
Weekly
Gross
Revenue
($1,000s)
Television
Advertising
($1,000s)
Newspaper
Advertising
($1,000s)
96
5
1.5
91
2
2
95
4
1.5
93
2.5
2.5
95
3
3.3
94
3.5
2.2
94
2.5
4.1
94
3
2.5
(a) Use α = 0.01 to test the hypotheses
H0:
β1 = β2 = 0
Ha:...

1. 60% of a department stores customers have a credit card from
that department store, and 30% of a store’s customers make at least
1 purchase per month on average. Finally, 80% of the customers who
make at least 1 purchase per month have a store’s credit card. Of
the customers who do not make at least 1 purchase per month, what
is the probability a randomly chosen customer has a store’s credit
card? (please round your answer to 4...

In an annual report to investors, an investment firm claims that
the share price of one of their bond funds had very little
variability. The report shows the average price as $12.00 with a
variance of 0.23. One of the investors wants to investigate this
claim. He takes a random sample of the share prices for 22 days
throughout the last year and finds that the standard deviation of
the share price is 0.4789. Can the investor conclude that the...

Recall that Benford's Law claims that numbers chosen from very
large data files tend to have "1" as the first nonzero digit
disproportionately often. In fact, research has shown that if you
randomly draw a number from a very large data file, the probability
of getting a number with "1" as the leading digit is about 0.301.
Now suppose you are an auditor for a very large corporation. The
revenue report involves millions of numbers in a large computer
file....

Recall that Benford's Law claims that numbers chosen from very
large data files tend to have "1" as the first nonzero digit
disproportionately often. In fact, research has shown that if you
randomly draw a number from a very large data file, the probability
of getting a number with "1" as the leading digit is about 0.301.
Now suppose you are an auditor for a very large corporation. The
revenue report involves millions of numbers in a large computer
file....

1/ A particular fruit's weights are normally distributed, with a
mean of 352 grams and a standard deviation of 28 grams.
If you pick 9 fruits at random, then 9% of the time, their mean
weight will be greater than how many grams?
Give your answer to the nearest gram.
2/A manufacturer knows that their items have a lengths that are
skewed right, with a mean of 7.5 inches, and standard deviation of
0.9 inches.
If 50 items are chosen...

1.)
A distribution of values is normal with a mean of 210 and a
standard deviation of 3.
Find the interval containing the middle-most 78% of scores:
Enter your answer accurate to 1 decimal place using interval
notation. Example: (2.1,5.6)
Hint: To work this out, 1) sketch the distribution, 2) shade the
middle 78% of the data, 3) label unkown data values on the
horizontal axis just below the upper and lower ends of the shaded
region, 4) calculate the...

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