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
ExtremeBDS [4]
3 years ago
13

The amount of water in a bottle is approximately normally distributed with a mean of 2.55 liters with a standard deviation of 0.

035 liter. Complete parts (a) through (d) below. a. What is the probability that an individual bottle contains less than 2.52 liters? Round to three decimal places as needed.) b. If a sample of 4 bottles is selected, what is the probability that the sample mean amount contained is less than 2.52 liters? (Round to three decimal places as noeded) c. If a sample of 25 bottles is selected, what is the probability that the sample mean amount contained is less than 2.52 liters? (Round to three decimal places as needed.) d. Explain the difference in the results of (a) and (c)
Mathematics
1 answer:
Natalka [10]3 years ago
3 0

Answer:

a) P(X

b) P(\bar X

c) P(\bar X

d) For part a we are just finding the probability that an individual bottle would have a value of 2.52 liters or less. So we can't compare the result of part a with the results for parts b and c.

If we see part b and c are similar but the difference it's on the sample size for part b we just have a sample size 4 and for part c we have a sample size of 25. The differences are because we have a higher standard error for part b compared to part c.

Step-by-step explanation:

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  The letter \phi(b) is used to denote the cumulative area for a b quantile on the normal standard distribution, or in other words: \phi(b)=P(z

Let X the random variable that represent the amount of water in a bottle of a population, and for this case we know the distribution for X is given by:

X \sim N(2.55,0.035)

a. What is the probability that an individual bottle contains less than 2.52 liters?

We are interested on this probability

P(X

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:

P(X

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.  

P(X

b. If a sample of 4 bottles is selected, what is the probability that the sample mean amount contained is less than 2.52 liters? (Round to three decimal places as noeded)

And let \bar X represent the sample mean, the distribution for the sample mean is given by:

\bar X \sim N(\mu,\frac{\sigma}{\sqrt{n}})

On this case  \bar X \sim N(2.55,\frac{0.035}{\sqrt{4}})

The z score on this case is given by this formula:

z=\frac{\bar x-\mu}{\frac{\sigma}{\sqrt{n}}}

And if we replace the values that we have we got:

z=\frac{2.52-2.55}{\frac{0.035}{\sqrt{4}}}=-1.714

For this case we can use a table or excel to find the probability required:

P(\bar X

c. If a sample of 25 bottles is selected, what is the probability that the sample mean amount contained is less than 2.52 liters? (Round to three decimal places as needed.)

The z score on this case is given by this formula:

z=\frac{\bar x-\mu}{\frac{\sigma}{\sqrt{n}}}

And if we replace the values that we have we got:

z=\frac{2.52-2.55}{\frac{0.035}{\sqrt{25}}}=-4.286

For this case we can use a table or excel to find the probability required:

P(\bar X

d. Explain the difference in the results of (a) and (c)

For part a we are just finding the probability that an individual bottle would have a value of 2.52 liters or less. So we can't compare the result of part a with the results for parts b and c.

If we see part b and c are similar but the difference it's on the sample size for part b we just have a sample size 4 and for part c we have a sample size of 25. The differences are because we have a higher standard error for part b compared to part c.  

You might be interested in
Can someone please help me with this because I don’t get it
yulyashka [42]

Answer:

161

Step-by-step explanation:

the sum of the two interior angles equals that exterior angle

121+40=161

8 0
3 years ago
Read 2 more answers
What is the answer!?
prisoha [69]
I think something wrong 
the answer must be 18
4 0
3 years ago
Read 2 more answers
Could someone please help me with this? Solution set of lx^2+mx+n=0 is...?
IgorLugansk [536]

Answer:

Simplifying

lx2 + mx + n = 0

Solving

lx2 + mx + n = 0

Solving for variable 'l'.

Move all terms containing l to the left, all other terms to the right.

Add '-1mx' to each side of the equation.

lx2 + mx + -1mx + n = 0 + -1mx

Combine like terms: mx + -1mx = 0

lx2 + 0 + n = 0 + -1mx

lx2 + n = 0 + -1mx

Remove the zero:

lx2 + n = -1mx

Add '-1n' to each side of the equation.

lx2 + n + -1n = -1mx + -1n

Combine like terms: n + -1n = 0

lx2 + 0 = -1mx + -1n

lx2 = -1mx + -1n

Divide each side by 'x2'.

l = -1mx-1 + -1nx-2

Simplifying

l = -1mx-1 + -1nx-2

Step-by-step explanation:

Hope this helped you!

6 0
3 years ago
Identify the Domain of each graph or table.
satela [25.4K]

Answer:

4 < x < 14

Step-by-step explanation:

................

3 0
3 years ago
today, 6 friends went out for lunch. their total Bill was $41.88, including tax and gratuity. they decide to split the Bill equa
Mariulka [41]
Each person will get back $3.02

4 0
3 years ago
Read 2 more answers
Other questions:
  • Subtracting a number is the same as adding its opposite.
    7·1 answer
  • Evaluate 2a - 3b for a = 7 and b = -2. 20 9 8
    10·1 answer
  • How do you simplify -24z2 divided by 6z
    15·2 answers
  • Of the following, which is the solution to 2x2 - 5x = -8?
    8·2 answers
  • Sushil was thinking of a number. Sushil adds 72 to the number, then doubles the result to get
    15·1 answer
  • Walt's monthly salary is $6,962.What would be his equivalent semimonthly salary?
    14·1 answer
  • PLEASE HELP ME easy algebra
    15·1 answer
  • Which expression is equivalent to 2(m − 5) + 6?
    15·2 answers
  • What is z in 3z - 18 = - 6
    7·2 answers
  • it takes Cynthia 12 hours to proof a chapter of Hawkes Learning Systems' Intermediate Algebra book and it takes Phillip 3 hours.
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!