1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Serjik [45]
3 years ago
5

An economist uses the price of a gallon of milk as a measure of inflation. She finds that the average price is $3.82 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?

b. what is the probability that the sample mean is between $3.78 and $3.86?

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 $3.92?
Mathematics
1 answer:
salantis [7]3 years ago
3 0

Answer:

(a) The standard error of the mean in this experiment is $0.052.

(b) The probability that the sample mean is between $3.78 and $3.86 is 0.5587.

(c) The probability that the difference between the sample mean and the population mean is less than $0.01 is 0.5754.

(d) The likelihood that the sample mean is greater than $3.92 is 0.9726.

Step-by-step explanation:

According to the Central Limit Theorem if we have an unknown population with mean <em>μ</em> and standard deviation <em>σ</em> and appropriately huge random samples (<em>n</em> > 30) are selected from the population with replacement, then the distribution of the sample means will be approximately normally distributed.

Then, the mean of the distribution of sample mean is given by,

\mu_{\bar x}=\mu

And the standard deviation of the distribution of sample mean is given by,

\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}

The information provided is:

n=40\\\mu=\$3.82\\\sigma=\$0.33

As <em>n</em> = 40 > 30, the distribution of sample mean is \bar X\sim N(3.82,\ 0.052^{2}).

(a)

The standard error is the standard deviation of the sampling distribution of sample mean.

Compute the standard deviation of the sampling distribution of sample mean as follows:

\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}

    =\frac{0.33}{\sqrt{40}}\\\\=0.052178\\\\\approx 0.052

Thus, the standard error of the mean in this experiment is $0.052.

(b)

Compute the probability that the sample mean is between $3.78 and $3.86 as follows:

P(3.78

                               =P(-0.77

Thus, the probability that the sample mean is between $3.78 and $3.86 is 0.5587.

(c)

If the difference between the sample mean and the population mean is less than $0.01 then:

\bar X-\mu_{\bar x}

Compute the value of P(\bar X as follows:

P(\bar X

                    =P(Z

Thus, the probability that the difference between the sample mean and the population mean is less than $0.01 is 0.5754.

(d)

Compute the probability that the sample mean is greater than $3.92 as follows:

P(\bar X>3.92)=P(\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}>\frac{3.92-3.82}{0.052})

                    =P(Z

Thus, the likelihood that the sample mean is greater than $3.92 is 0.9726.

You might be interested in
Find all the solutions of sin2x-sinx=0
Lady_Fox [76]

x=πn

π/3+2πn

5π/3+2πn

for any integer n

7 0
3 years ago
Randomly meeting someone whose social security number ends in the same digit as yours
Galina-37 [17]
That is very cool and rare if you did it nice job!
3 0
3 years ago
Read 2 more answers
What is 6,051 x 10^5 written in standard form?
Setler79 [48]

Answer:

605100

Step-by-step explanation:

6.051*10^5=605100

6 0
3 years ago
A certain bank balance b is given by b= 100+d-w where d is deposits and w is withdrawls. What is the balance when d =100 and w=1
expeople1 [14]
You know that d = 100 and w = 125, so you plug that into the equation and solve as shown:
b= 100 + d - w
  = 100 + 100 - 125
  = 200 - 125
  = $75
You now have $75 left as balance.
3 0
3 years ago
Read 2 more answers
I need help with multi step inequalities
vodomira [7]

either

-(3x+3)-2x (less than) -4(x-2)-2

-3x+3-2x (less than) -4x +8-2

-5x+3 (less than)-4x+6

Or if you need it simplified

-5x +3 (less than) -4x+6

+4x                           4x

-x+3 (less than) 6

    -3                  -3

-x(less than) 3

(-x/-1) Less than (3/-1)

x (less than) -3

(didnt have the less than greater than sign so typed it)

6 0
3 years ago
Other questions:
  • What type of triangle will have a circumcenter outside the triangle?
    6·1 answer
  • Math help plz!!!
    12·2 answers
  • Name the intesection of lines r and s?
    12·2 answers
  • Legs = 20 mm and 27 mm<br> a? + b2 = c2<br> 2 points<br> YOUR QUESTION:<br> 6<br> 20 mm<br> 27 mm
    9·1 answer
  • If a dice is rolled 18 times, how many times is the number 2 expected to come up? *
    9·1 answer
  • Yx divide 2 use x=7 and y=2
    14·1 answer
  • Please help please pls
    10·2 answers
  • A water tanklalready contains
    11·1 answer
  • John had $20. He earned $5, spent $10, earned $5 again, and then spent $3. After this series of earnings and expenses, how much
    7·1 answer
  • What is the factored form of this expression? <br><br> -9x^3-12x^2-4x
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!