(Solved) Business Statistics II: What is the probability...

jgosset2

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6 years ago

Business Statistics II: What is the probability...

An economist uses the price of a gallon of milk as a measure of inflation. She finds that the average price is $3.50 per gallon and the population standard deviation is $0.33. You decide to sample 40 convenience stores, collect their prices for a gallon of milk, and compute the mean price for the sample.

a. What is the standard error of the mean in this experiment? (Round your answer to 4 decimal places.)

Standard error: .0522

b. What is the probability that the sample mean is between $3.46 and $3.54? (Round z value to 2 decimal places. Round your final answer to 4 decimal places.)

Probability?

c. What is the probability that the difference between the sample mean and the population mean is less than $0.01? (Round z value to 2 decimal places. Round your final answer to 4 decimal places.)

Probability?

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jgosset2 Author

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6 years ago

Part C is not the correct answer. The rest is perfect.

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bio_man

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Educator

6 years ago

Quote

A. What is the standard error of the mean in this experiment?

B. What is the probability that the sample mean is between $3.46 and $3.54?

C. What is the probability that the difference between the sample mean and the population mean is less than 0.01?

D. What is the likelihood the sample mean is greater than $3.60?

Answers:

(A) Standard error = s/vn =0.33/sqrt(40) =0.05217758

(B) P(3.46 <xbar< 3.54)

= P((3.46-3.5)/0.05217758 <(xbar-mean)/(s/vn) <(3.54-3.5)/0.05217758)

=P(-0.77 <Z< 0.77)

=0.5587

(C) P(xbar-mean <0.01) = P((xbar-mean)/(s/vn) <0.01/0.05217758)

=P(Z<0.19)

=0.5753

(D) P(xbar>3.6) = P(Z>(3.6-3.5)/0.05217758)

=P(Z>1.92)

=0.0274

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jgosset2 Author

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6 years ago

But that's the same answer you gave the last time for part C.

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bio_man

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Educator

6 years ago

Try this:

(B) mean = 3.5, standard error = 0.05217

for 3.46, z = (3.46-3.5)/0.05217 = -0.7667

for 3.54, z = (3.54-3.5)/0.05217 = 0.7667

P(3.46<mean <3.54) = P(-0.7667<z<0.7667) = 0.7784-0.2216 = 0.5568

as P(z>-0.7667) = 0.7784 and P(z>0.7667) 0.2216

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jgosset2 Author

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6 years ago

No this one: c. What is the probability that the difference between the sample mean and the population mean is less than $0.01? (Round z value to 2 decimal places. Round your final answer to 4 decimal places.)

Probability?

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bio_man

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Educator

6 years ago

My bad

P =? for means between 3.5 - 0.01 = 3.49 and 3.5 + 0.01 = 3.51

Proceeding as in (b), we get P(3.49<mean< 3.51) = 0.152

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jgosset2 Author

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6 years ago

Nope, the correct answer was .1506
No idea how to get it though... :/
I hate stats....

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bio_man

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Educator

6 years ago

That's what I got. Their answer is rounded to 3 significant digits.

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123physics

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#10

4 years ago

thx

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destiny g.

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#11

4 years ago

This was so helpful!

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KitSoN B.

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#12

3 years ago Edited: 3 years ago, KitSoN Bowie

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endcrow

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#13

3 years ago

THANKS GREAT WEBSITE.

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