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
-Dominant- [34]
3 years ago
14

The distribution of weights of potato chip bags filled off a production line is unknown. However, the mean is m=13.35 OZs and th

e standard deviation is s=.1200 OZs. To check the quality of the potato chip bags, a random sample of n=36 bags is selected. Use `X to denote the sample mean.A) The mean (or expected value) of the sample mean `X isa.13.23b.13.00c.13.47d.13.50e.none of the aboveB) The standard deviation of the sample mean `X isa.0.0200b.0.1200c.0.0600d.0.3600e.none of the aboveC) The probability that the sample mean `X is less than or equal to 13.38 OZs is closest toa.0.0668b.0.0998c.0.4332d.0.9332e.none of the aboveD) The probability that the sample mean `X is less than or equal to 13.32 OZs is closest toa.0.0668b.0.0998c.0.4332d.0.9332e.none of the aboveE) The probability that the sample mean `X is between 13.30 and 13.36 OZs is closest toa.0.0062b.0.3085c.0.6853d.0.4938e.none of the above
Mathematics
1 answer:
Nikitich [7]3 years ago
8 0

Answer:

a) \mu_{\bar X} =13.35

e.none of the above

b) \sigma_{\bar X}= \frac{0.12}{\sqrt{36}}= 0.02

a.0.0200

c) z = \frac{13.32-13.35}{\frac{0.12}{\sqrt{36}}}= -1.5

P(\bar X< 13.32)= P(z

a.0.0668

d) z = \frac{13.30-13.35}{\frac{0.12}{\sqrt{36}}}= -2.5

z = \frac{13.36-13.35}{\frac{0.12}{\sqrt{36}}}= 0.5

P(13.30

c.0.6853

Step-by-step explanation:

Previous concepts

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 central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

Solution to the problem

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

X \sim N(13.35,0.12)  

Where \mu=13.35 and \sigma=0.12

From the central limit theorem we know that the distribution for the sample mean \bar X is given by:

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

Part a

\mu_{\bar X} =13.35

Part b

\sigma_{\bar X}= \frac{0.12}{\sqrt{36}}= 0.02

Part c

We want this probability:

P(\bar X< 13.32)

For this case we can use the z score formula given by:

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

And using this formula we got:

z = \frac{13.32-13.35}{\frac{0.12}{\sqrt{36}}}= -1.5

P(\bar X< 13.32)= P(z

Part d

We want this probability:

P(13.30

For this case we can use the z score formula given by:

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

And using this formula we got:

z = \frac{13.30-13.35}{\frac{0.12}{\sqrt{36}}}= -2.5

z = \frac{13.36-13.35}{\frac{0.12}{\sqrt{36}}}= 0.5

P(13.30

You might be interested in
Show me how to work the equation for 6×+20=-4​
jek_recluse [69]

Answer:

<h2>x = -8/3</h2>

Step-by-step explanation:

6x + 20 = -4

subtract 20 from both sides

6x = -16

divide by 2

3x = -8

<h2>x = -8/3</h2>
3 0
3 years ago
Read 2 more answers
Mary throws a plastic disc to her friend, which her friend catches six seconds after Mary throws it. The table shows the height
natta225 [31]
Unfortunately, there is no given table. However, assuming no air resistance, the projectile moves in constant acceleration in the y-axis, while constant velocity in the x-axis. If the total time of flight is 6 seconds, then at 3 seconds the reaches its maximum height. Also, there is no given initial velocity, which means any useful calculation is impossible.
8 0
2 years ago
Read 2 more answers
Select all the correct answers.
Nesterboy [21]

Answer:

D. 75(5r+3d+4f) and 75(5r)+75(3d)+75(4f)

5 0
2 years ago
Ben is buying a tiny house. He will borrow $23,000 at a rate of 3% per year for 4 years. If the interest is compounded annually,
uranmaximum [27]

Answer:

$25,886.70

Step-by-step explanation:

8 0
2 years ago
Given that f(x) is even and g(x) is odd, determine whether each function is even, odd, or neither. (f • g)(x) = ? (g • g)(x) = ?
vekshin1

Answer:

<h2>(f · g)(x) is odd</h2><h2>(g · g)(x) is even</h2>

Step-by-step explanation:

If f(x) is even, then f(-x) = f(x).

If g(x) is odd, then g(-x) = -g(x).

(f · g)(x) = f(x) · g(x)

Check:

(f · g)(-x) = f(-x) · g(-x) = f(x) · [-g(x)] = -[f(x) · g(x)] = -(f · g)(x)

(f · g)(-x) = -(f · g)(x) - odd

(g · g)(x) = g(x) · g(x)

Check:

(g · g)(-x) = g(-x) · g(-x) = [-g(x)] · [-g(x)] = g(x) · g(x) = (g · g)(x)

(g · g)(-x) = (g · g)(x) - even

7 0
3 years ago
Read 2 more answers
Other questions:
  • Write 27 : 28 as a ration in its simplest form
    14·2 answers
  • The volume (V) of a sphere varies directly with the cube of its radius (r). If k is the constant of proportionally, which is the
    14·1 answer
  • Suppose a1={1,{2}}a1={1,{2}} and a2={∅,{1,2}}a2={∅,{1,2}} and a3={∅,{1},2}a3={∅,{1},2}. enter "t" for each true, and "f" for eac
    10·1 answer
  • Which has the same value as 15 tens
    6·2 answers
  • Simplify 3 to the second exponent ⋅ 3 to 5th the exponent .
    8·1 answer
  • Paul is making loaves of raisins bread to sell at a fundraiser event the recipe calls for 1/3 cup of raisins for each loaf and P
    14·1 answer
  • The distance S that a certain object falls from a height of 350 ft in T seconds is given by the following formula.
    5·1 answer
  • Use the graph below for this question:
    6·1 answer
  • 5/6 divided 2/3 pls help
    12·1 answer
  • How now why would a prism beat a sphere in a competion
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!