Concerns about climate change and CO2 reduction have initiated the commercial production of blends of biodiesel (e.g., from renewable sources) and petrodiesel (from fossil fuel). Random samples of 32 blended fuels are tested in a lab to ascertain the bio/total carbon ratio. (a) If the true mean is .9370 with a standard deviation of 0.0090, within what interval will 99 percent of the sample means fall

Answer:

99% of the sample means will fall between 0.93288 and 0.94112.

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 [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

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 p-value, 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 [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

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

The true mean is .9370 with a standard deviation of 0.0090

This means that [tex]\mu = 0.9370, \sigma = 0.0090[/tex]

Sample of 32:

This means that [tex]n = 32, s = \frac{0.009}{32} = 0.0016[/tex]

Within what interval will 99 percent of the sample means fall?

Between the 50 - (99/2) = 0.5th percentile and the 50 + (99/2) = 99.5th percentile.

0.5th percentile:

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

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]-2.575 = \frac{X - 0.9370}{0.0016}[/tex]

[tex]X - 0.9370 = -2.575*0.0016[/tex]

[tex]X = 0.93288[/tex]

99.5th percentile:

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

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]2.575 = \frac{X - 0.9370}{0.0016}[/tex]

[tex]X - 0.9370 = 2.575*0.0016[/tex]

[tex]X = 0.94112[/tex]

99% of the sample means will fall between 0.93288 and 0.94112.

Given: −3(a–b) < 0, which is the greater: a or b? Give numerical examples.

cacula las dimensiones de un rectangulo sabiendo que su area es de 66cm y su base mide 5cm mas que su altura

Use the triangle above to find the measure of angle A.

Does Allena uses 1/2 gallon or less than 1/2 of water

i need a reduced mixed number from 12(x-6)=2(x-9)

2 : 6 : 7 = x : 36 : y

1. A store priced a textbook at $126.75 using a markup of 34% of cost.

What was the cost of the book?
What is the markup as a percent of selling price?
2. The Tea Spot sells stove top kettles at a markup of 15% of the selling price. The store’s margin on a particular model is $6.87.

What is the selling price of the kettles?

What is the cost of buying the kettles?

3. What is the rate of markup based on cost? An eyeware shop sells wrap around sunglasses for $86. If they wanted to lower the price to $75, what rate of markdown would they have to offer?

4. The Music Box paid $13.95 for a DVD. Expenses are 17% of the selling price and the required profit is 14% of selling price. During a weekend sale, the DVD was marked down 10%.

What was the regular selling price?

What was the sale price?

What was the operating profit or loss?

5. Harry’s Hardware realizes a markup of $34.50 if it sells an article at a markup of 40% of the selling price.

What is the regular selling price?

What is the cost?

What is the rate of markup based on cost?

If overhead expenses are 27% of cost, what is the break-even price?

What is the operating profit or loss, if the article is sold for $75?

6. Autobots purchases car stereos for $225 less 331⁄3%. The store operates at a normal markup of 35% of regular selling price. The owner marks all merchandise with new regular selling prices so that the store can offer a 18 2⁄3% discount while keeping the same gross profit. a) What is the original regular selling price? b) What is the new selling price?

A patio table set that cost a dealer$330 less 45%, 25% is markedup 160% of cost. For quick sale, the table set was reduced 35%.

What is the regular selling price?

What is the sale price?

What is the rate of markup based on cost realized during the sale?

Grin & Bare It buys briefs for $15 less 15%, 10%. The briefs are priced at a regular selling price to cover expenses of 22% of regular selling price and a profit of 15% of regular selling price. For a special weekend sale, briefs were marked down 20%.

What was the operating profit or loss on briefs sold during the weekend sale?

What rate of markup was realized based on cost?

Ming Wu bought knifesets for $170 less 40%, 162⁄3%, 10%. The store’s

overhead is 45% of regular selling price and the profit required is 21.25% of regular selling price

What is the break-even price?

What is the maximum rate of markdown the store can offer to break even?

What is the realized rate of markup based on cost if the knife sets are sold

at the break-even price?

10. A shoe store bought 225 pairs of shoes for $15750. Twenty-five pairs were sold

at a markup of 150% of cost and 175 pairs at a markup of 75% of cost; 10 pairs were sold during a clearance sale for $80 each and the remaining shoes were disposed of at 20% below cost. Assume all pairs of shoes had the same cost.

a. What was the cost of shoes?
b. What was the amount of markup realized on the purchase? c. What was the percent markup based on selling price?

9
28.26

28.26
4.5

4.5
28.26

28.26
9

it’s a FRATION the first number is on top of the line and the other number is on the bottom

Use the substitution method for solve for x and y.


y = 2x + 10
y = -4x - 2

PLEASE I NEED HELP I GOT A PUPPY AND IM EXHAUSTED HE DOESNT SLEEP AT NIGHT

Manny's muffins sells 50 muffins each day. 12 of these are blueberry. If they sell a 150 muffins tomorrow, how many blueberry muffins can they expect to sell?

The area of a rectangular living room is 99 square feet. The width of the room is 9 feet. What is the perimeter of the room?

please help im literally crying im desperate i can't fail please ​

Find the value of x in each diagram.

can you help me with this ​

what are all the powers of 4 in the range 4 through 1,000​

Which equation describes the function in the table below?

Stevie bought a bag of lollipops. The bag contained 30 lollipops and 6 of them were grape flavored. What percent of the lollipops were grape flavored?​

Indicate whether the function represents an exponential growth or decay.

Find the measure of 2.
63° 117°
62 = [?]
Enter

Help pls!!!! Pls explain how you got the answer if you can!!! Have a blessed day
Also if you don’t know the exact answer answer and comments. And pls don’t waste my points this assignment is very important

Plz help I put a pic there for u

WHO WANTS BRAINLIEST FOR HELPING ME!
also can u explain how to solve ;[

Which of these is the domain and range
for the parent function of 2(x-5)° +3 ?

Write this polynomial in standard form:
x^5-6x^5+8x^4

a fruit company delivers its fruit in two typed of boxes: large and small. A delivery of 2 large boxes and 3 small boxes has a total weight of 72 kilograms. A delivery of 6 large boxes and 5 small boxes has a total weight of 162 kilograms. How much does each type of box weigh?

Find the sum of 5X +20 and the opposite of 20
________ _________ ________

What are 2 factors of 72y + 108z?

Subtract the following expression (12x+6)-(5x+2)​

How can I figure this out? What is |-9-3|?