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
Illusion [34]
3 years ago
5

Concerns about the climate change and CO2 reduction have initiated the commercial production of blends of biodiesel (e.g. from r

enewable sources) and petrodiesel (from fossil fuel). Random samples of 34 blended fuels are tested in a lab to ascertain the bio/total carbon ratio.(a) If the true mean is 0.9370 with a standard deviation of 0.0090 within what interval will 99% of the sample means fail?(b) If the true mean 0.9370 with a standard deviation of 0.0090, what is the sampling distribution of ¯X?
Mathematics
1 answer:
natta225 [31]3 years ago
6 0

Answer:

a) 99% of the sample means will fall between 0.933 and 0.941.

b) By the Central Limit Theorem, approximately normal, with mean 0.937 and standard deviation 0.0015.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

(a) If the true mean is 0.9370 with a standard deviation of 0.0090 within what interval will 99% of the sample means fail?

Samples of 34 means that n = 34

We have that \mu = 0.937, \sigma = 0.009

By the Central Limit Theorem, s = \frac{0.009}{\sqrt{34}} = 0.0015

Within what interval will 99% of the sample means fail?

Between the (100-99)/2 = 0.5th percentile and the (100+99)/2 = 99.5th percentile.

0.5th percentile:

X when Z has a pvalue of 0.005. So X when Z = -2.575.

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

-2.575 = \frac{X - 0.937}{0.0015}

X - 0.937 = -2.575*0.0015

X = 0.933

99.5th percentile:

X when Z has a pvalue of 0.995. So X when Z = 2.575.

Z = \frac{X - \mu}{s}

2.575 = \frac{X - 0.937}{0.0015}

X - 0.937 = 2.575*0.0015

X = 0.941

99% of the sample means will fall between 0.933 and 0.941.

(b) If the true mean 0.9370 with a standard deviation of 0.0090, what is the sampling distribution of ¯X?

By the Central Limit Theorem, approximately normal, with mean 0.937 and standard deviation 0.0015.

You might be interested in
Help me prettyyyy please
OlgaM077 [116]

Answer:

Hii! Surface area= 207.35, volume= 226.19. Hope this helps!

3 0
3 years ago
Read 2 more answers
The number +10 can be used to indicate a
Serhud [2]
The number + 10 can be used to indicate a  : 
10 degree rise in temperature.

Temperature can be measured in Kelvin , Celsius, and Fahrenheit. In all measurement, + number indicate a rise in the temperature
4 0
2 years ago
56 is 75% of what number
motikmotik
56 is 75% of 74.6667

Convert the percentage into a decimal by dividing it over 100:
\frac{75}{100} = 0.75

Divide 56 over 0.75:
\frac{56}{0.75} = 74.6667
8 0
3 years ago
A group was selling tickets for their fundraising event. For the first day of the event, they sold 30 pre-sale tickets and 45 ti
goldfiish [28.3K]

Answer:

4

Step-by-step explanation:

4 0
3 years ago
A 60$ purse is on sale for 10% give the sell price
Nana76 [90]

Answer:$54

Step-by-step explanation:

60(0.9) = $54

5 0
2 years ago
Read 2 more answers
Other questions:
  • How do I solve this ?
    13·1 answer
  • Adam uses coconut milk for the dessert.
    7·1 answer
  • Select the equation of the line parallel to the equation y = -2x - 7 that passes through the point (3, 1).
    11·1 answer
  • Wendy is arranging books on the bookshelves in the school library. The total number of books she arranges is given by the equati
    5·1 answer
  • The population of a town grows at a rate proportional to the population present at time t. The initial population of 500 increas
    6·1 answer
  • Quadrilateral PQRS is inscribed in a circle , as shown. Which statement is true?
    7·1 answer
  • Bill and Amy want to ride their bikes from their neighborhood to school which is 14.4 km away. It takes Amy 40 minutes to arrive
    14·1 answer
  • Hi does anyone know the answer?
    14·1 answer
  • I'm using system of equations and I have to use either substitution or elimination. My two equations are
    13·1 answer
  • You work for a company that makes tiles for patios. A customer sent you the following picture of his patio. He said the patio is
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!