Suppose the weights of Farmer Carl's potatoes are normally distributed with a mean of 8.0 ounces and a standard deviation of 1.1 ounces.
(a) If 5 potatoes are randomly selected, find the probability that the mean weight is less than 9.3 ounces? Round your answer to 4 decimal places.
(b) If 6 potatoes are randomly selected, find the probability that the mean weight is more than 9.0 ounces? Round your answer to 4 decimal places.
Answer:
a) 0.9959 = 99.59% probability that the mean weight is less than 9.3 ounces
b) 0.0129 = 1.29% probability that the mean weight is more than 9.0 ounces
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 zscore 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 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 [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.
Mean of 8.0 ounces and a standard deviation of 1.1 ounces.
This means that [tex]\mu = 8, \sigma = 1.1[/tex]
(a) If 5 potatoes are randomly selected, find the probability that the mean weight is less than 9.3 ounces?
[tex]n = 5[/tex] means that [tex]s = \frac{1.1}{\sqrt{5}} = 0.4919[/tex]
This probability is the pvalue of Z when X = 9.3. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{9.3 - 8}{0.4919}[/tex]
[tex]Z = 2.64[/tex]
[tex]Z = 2.64[/tex] has a pvalue of 0.9959
0.9959 = 99.59% probability that the mean weight is less than 9.3 ounces
(b) If 6 potatoes are randomly selected, find the probability that the mean weight is more than 9.0 ounces?
[tex]n = 6[/tex] means that [tex]s = \frac{1.1}{\sqrt{6}} = 0.4491[/tex]
This probability is 1 subtracted by the pvalue of Z when X = 9. So
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{9 - 8}{0.4491}[/tex]
[tex]Z = 2.23[/tex]
[tex]Z = 2.23[/tex] has a pvalue of 0.9871
1 - 0.9871 = 0.0129
0.0129 = 1.29% probability that the mean weight is more than 9.0 ounces
To charter a fishing boat for 3 hours the captain charges a base fee of 45.00 plus 15.00 per person using variables construct a function that models the total cost of a 3-hour charter in terms of the number of people in your function. Define any variables you use. What is the correct interpretation of the initial value snd the rate of change
Answer:
$90.00
Step-by-step explanation:
Given
[tex]c = 45.00[/tex]--- base fee
[tex]m = 15.00[/tex] --- rate
[tex]x = 3[/tex] --- individuals
Required
Determine the total amount paid (y)
The relationship between the variables is:
[tex]Total = Base\ Fee + Rate * Individuals[/tex]
[tex]y = c + mx[/tex]
This gives:
[tex]y = 45.00 + 15.00 * 3[/tex]
[tex]y = 45.00 + 45.00[/tex]
[tex]y = 90.00[/tex]
Hence, the amount is $90.00
Which equation represents a line with slope -1/2
that passes through (-3, 4) ?
Answer:
y=-1/2x+5/2
Step-by-step explanation:
y-4=-1/2(x-(-3))
y-4=-1/2(x+3)
y-4=-1/2x-3/2
y=-1/2x-3/2+4
y=-1/2x+5/2
Find f(-3)
Please help!
Answer:
-6
Step-by-step explanation:
anything for sangwoo
The numeric value of this expression is -6!
To find out what the value of this expression is, let's replace f(x) with f(-3) and perform the given math operations.[tex] \large \sf f(x) = 12 - 2x {}^{2} [/tex]
[tex] \large \sf f(-3) = 12 - 2\cdot (-3){}^{2} [/tex]
[tex] \large \sf f(-3) = 12 - 2\cdot 9 [/tex]
[tex] \large \sf f(-3) = 12 - 18 [/tex]
[tex] \boxed{ \boxed{{ \large \sf f(-3)=-6}}}[/tex]
Therefore, the result of this expression is f(-3)=-6. ✅
a polygon has 10080° as the total interior angle how many sides has the polygon
The formula for the sum of the interior angles of a polygon is (n - 2) * 180. In this formula, N is the number of sides. So, to find the number of sides that a polygon with an interior angle measure of 10080 has, we'll set the formula equal to 10080.
10080 = (n - 2) * 180
Divide both sides by 180
56 = n - 2
Add 2 to both sides
n = 58
Hope this helps!! :)
Answer:
58 sides
Step-by-step explanation:
The sum of the interior angles of a polygon is 10,080°
n = the number of sides
(2n - 4)90 = 10080
2n - 4 = 10080/90 = 112
2n = 116
n = 58.
Write The Equation on the line.
Answer:
Check pdf
Step-by-step explanation:
Match each equation on the left to the mathematical property it uses on the right
Answer:
attachment plz
Step-by-step explanation:
nothing is being seen
need these 2 questions answer fast pls
Answer:
4a) The sides are not scaled up equally for the sides. Plus, B is not a right triangle since it does not satisfy the pythogorean theorem.
4b) 6, 8, 10
What do I do for this
Answer:
its 7 or B.
Step-by-step explanation:
7 is the number being repeated the most (dunno if that makes sense so the mode is the most common number in a data set.)
2.
Akeem is making juice for a class party. For every 1 litre of water, he uses 100 ml of juice
mix
If he uses 4 litres of water, how many ml of juice does he use?
Answer:
400ml of juice
Step-by-step explanation:
1 litre of water = 100ml of juice
4 litres of water =? ml of juice
to get from 1 litre to 4 litre of water you multiply by 4,so you do the same for the juice and multiply the juice by 4.
100×4=400
4 litres of water = 400ml of juice
Pls help I will give brainiest answer.
Answer:
1) D
2) A
Step-by-step explanation:
Complete the equation of the line through (-10.-7) and (5.9).
15 POINTS PLEASE
Answer:
y=16/15x-11/3
Step-by-step explanation:
(9--7)/(5--10)
slope = 16/15
y=16/15(x)+b
-9=(16/15)(-5)+b
b=-11/3
What is the slope of the line?
y+3 = -4(2 + 7)
Answer:-4
Step-by-step explanation:
The temperature of a piece of metal was 32°C. It was then lowered into a glass of
hot water and the temperature of the piece of metal rose to 36°С. Find the
percentage increase in the temperature of the piece of metal.
Answer:
12.5%
Step-by-step explanation:
Given that,
Initial temperature of a piece of metal = 32°C
Final temperature of the piece of metal = 36°С
We need to find the percentage increase in the temperature of the piece of metal. The percentage increase in any value is given by the relation as follows :
[tex]\%=\dfrac{|\text{final value-initial value}|}{\text{initial value}}\times 100\\\\=\dfrac{36-32}{32}\times 100\\\\=12.5\%[/tex]
So, the required percentage increase in the temperature of the piece of metal is equal to 12.5%.
What is 472 x 82 i also need your thiniing process
Answer:
472×82=38704
Step-by-step explanation:
Prime factorization:
2^4×41×59
What property or theorrm would we have to use on these triangles to make them congruent
by ASA shortcut?
==============================================================
Explanation:
The diagram shows that we have two pairs of angles that are congruent. The angles with the single red arc pair up and are congruent, and the angles with the double arcs are the other congruent pair.
That takes care of the two "A"s in "ASA". As you can probably guess or know by now, "A" stands for "angle".
The only thing we need is the info about a pair of sides if they are congruent or not. In this case, we can see that the horizontal sides of the triangles are congruent since they overlap perfectly, or they are a shared common side. We use the reflexive property to say that "any segment is congruent to itself".
This is a question my friend asked me help
Cranberry juice is made with a 16:3:1 ratio of water:sugar:cranberries. How much water, in gallons, is needed in order to make three gallons of cranberry juice? Express your answer as a common fraction.
Answer:
12 / 5 gallons
Step-by-step explanation:
look at the picture nd hurry please it needs to be done by 3 I have to do reading too!
Answer:
First one
Step-by-step explanation:
Even numbers
2 is tossed 10 times
4 is tossed 10 times
6 is tossed 9 times
10 + 10 + 9 = 29
Odd numbers
1 is tossed 8 times
3 is tossed 6 times
5 is toosed 7 times
8 + 6 + 7 = 21
A set of buttons sells for $2.75 and costs $0.55 to make. Twenty percent of the profit (the difference between the purchase price and the amount it costs to make) from each set of pencils goes to RMS. If 500 sets are sold, what is the amount of money that will go to the school? i will give brainlyest A
$195.00
B
$220.00
C
$275.00
D
$310.00
Answer: b
Step-by-step explanation: I am 95% sure
Jacob designs a building with a square base. He starts by building a model for the building, which has a base with an
area of 36 feet?. The base of the real building will have an area of 6084 ft.?.
What is the scale factor between the model and the real building?
O 78
O 13
O 169
O 6
Answer:
Step-by-step explanation:
base of model is 6 ft by 6 ft
base of building is 78 ft by 78 ft
scale factor = 78÷6 = 13
What is the difference between a savings and a checking account? HELPPP?!
1.A checking account creates interest.
2.A savings account creates Interest.
3.A savings account lets you take out as much money as you want as many times as you want.
4.Both accounts are the sam.
Answer:
3
Step-by-step explanation:
A color printer prints 10 pages in 4 minutes. How many minutes does it take per page?
Answer:
2/5 minute OR 24 seconds
Step-by-step explanation:
4/10 = 2/5 minute
Hope that helps!
cost of 4 dozen bananas is rupees 180 how many bananas can be purchased for rupees 30 unto
Answer:
8 bananas
Step-by-step explanation:
4 dozen is equal to 48 and 180 divided by 48 is 3.75 then 30 divided by 3.75 is 8
Doug rents a kayak for 12 days the rental charges 18 per day what is the best estimate for the total cost of the kayak rental
Answer:
200
Step-by-step explanation:
I rounded both numbers and multiplayer them.
a) 7l - 15 = 6
b) 3j -18=3
c) 5k+7=32
d) 9m+11=74
e) 6n+12=72
f) 7r-8=41
j) 6q-12=84
h) 3k+7=46
I) 5m+12=72
k) 9n+9=72
l) 6r-8=40
m) 11q-10=89
A baby girl weighed 6 pounds at birth and 8
pounds one month later. How many ounces
did the baby gain in her first month of life?
A. 16 ounces
В.
64 ounces
C. 32 ounces
D. 48 ounces
Answer: C
Step-by-step explanation:
1 pound is equivalent to 16 ounces. She earned 2 pounds in 1 month, meaning that you have to multiply 16 times 2, which gives 32 ounces. Hope this can help you! Have a great day/night!
2x=11 need the answer plss
Answer:
x=11/2 = 5 1/2
Step-by-step explanation:
Answer:
5.5 =x
Step-by-step explanation:
2x=11
1. Start by dividing by ten since its a even number
2. Then you'll get 5
3. With the last number you'll divide it that'll end up with
.5
4. Just combine both 5 and .5 and you'll get your answers 5.5
An item originally costs $175.00. The item is now on sale for 99.75. What percent is the sale price for the original price? Is this an example of percent increase or decrease? Explain how you know?
Answer:
Discount percent = 43% off
Discount amount (money saved) = $75.25
Step-by-step explanation:
To find the discount percentage:
List price ($175) minus the sale price ($99.75) then divided by the list price ($175) and multiplied by 100 to get the discount percent of 43%.
To find how much money was saved:
List price ($175) minus sale price ($99.75) to get the amount saved, which savings are $75.25 in this case.
I hope this helps :)
Solve the triangle. Round your answers to the nearest tenth.
Answer:
Area = 80 units²
Step-by-step explanation:
Given that:
a = 19 units
b = 9 units
c = 97°
Find the area of the triangle!
Area = ab(sin(c))/2
Area = [19×9×(sin(97))]/2
Area = 84.86 units²
Area = 80 units² ✅
______________
#IndonesianPride
- kexcvi -
Which is the closest synonym for the word productive?
Press enter to interact with the item, and press tab button or down arrow until reaching the Submit button once the item is selected:
A.) Mysterious
B.) Cheerful
C.) Confident
D.) Valuable
Answer:
The answer would be letter D. Valuable.