The cost to produce a batch of granola bars is approximately Normally distributed with a mean of $7.19 and a standard deviation of $0.86. If a random sample of 12 batches of granola bars is selected, what is the probability that the mean cost will be more than $7.00?
0.2220
0.2339
0.7653
0.7780
Answer:
0.7780
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use 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.
Population:
We have that [tex]\mu = 7.19, \sigma = 0.86[/tex]
Sample of 12:
[tex]n = 12, s = \frac{0.86}{\sqrt{12}} = 0.2483[/tex]
What is the probability that the mean cost will be more than $7.00?
This is 1 subtracted by the pvalue of Z when X = 7. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{7 - 7.19}{0.2483}[/tex]
[tex]Z = -0.765[/tex]
[tex]Z = -0.765[/tex] has a pvalue of 0.222
1 - 0.222 = 0.778
So the answer is 0.7780
determine whether the following graph represents a function , ILL MARK BRAINLIST
Answer:
this is not a function
Step-by-step explanation:
add fractions 17/3+5/2=
Answer:
answer is below
Step-by-step explanation:
49/6 or 8 1/6
Jordan gave her basil plant 86 milliliters of water yesterday. How many liters of liquid did she give her plants
Answer: 0.086
Explanation: There are 1,000 milliliter in a liter. Since 86 is below 1,000, your answer won’t be in front of the decimal. For example, if you had 3,000 milliliters, your answer would be 3.0 liters.
The ratio of two numbers is 7:5. The product of these numbers is 140. What is the smaller if these two numbers?
Step-by-step explanation:
7x×5x=140
35x²=140
x²= 4
x=2
Smaller number = 5x = 5×2=10
Hope this helps you.
At the football game, 8 out of every 20 spectators were girls. There were a total of 1560 spectators at the game.
How many of the spectators were girls?
Ο Α. 130
Ο Β. 195
C. 624
D. 736
Ε. 1040
Answer:624
Step-by-step explanation:
k ≥0
plz help
what is it?
[tex]\text{Hey there!}[/tex]
[tex]\bold{The\ result\ should\ be\ the\ same\ thing\ as\ the\ equation... You\ don’t}\\\bold{have\ enough\ information\ to\ solve\ for\ it!}[/tex]
[tex]\boxed{\bold{Answer: k\geq 0\boxed{\bold{It\ is\ a\ CLOSED\ circle\ SHADED\ to\ the\ RIGHT}}}}\huge\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1048}[/tex]
Nick works forty hours per week, thirty-five of those hours are paid at the basic rate of
pay (£10 per hour) and the remaining five hours are paid as over-time (£15 per hour).
What is the ratio of basic pay to over-time pay?
Answer:
1:1.5
Step-by-step explanation:
if 10:15 when we divide both sides by 10 w get 1:1.5
explain why 15 + 1/2n is an algebraic expression
The expression 15 + 1/2n is an algebraic expression because, the expression contains a variable and this variable is Variable n.
Discussion:
A determining factor for concluding which expression is algebraic or not is the presence or absence of a variable.
However, in this case, the expression, 15 + 1/2n is an algebraic expression due to the fact that it contains a variable, n.
Read more on algebraic expressions;
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which value is the best estimate for x?
A=24.4
B=27.0
C=63.0
D=65.6
PLEASE HELP Show your work to find the measure of angle L.
Answer:
if I am guessing this is trigonometry
First is to look at what sides you have in which you have the legs. This means you can use tangent. how ever you need to use arctangent or
tan^-1 to find the angle.
the way you set this up in your calculator is tan^-1(8.4÷15.2). plus be sure it's on Deg not Rad.
This leaves the answer if 28.9°
I hope this helps.
An environmental study was conducted. It reported that houses with more inhabitants do not necessarily produce more or less trash. What can be determined?
A. There is no correlation between number of inhabitants and amount of trash produced.
B. There is a correlation between number of inhabitants and amount of trash produced. However, there is no causation. This is because there is probably an increase in the amount of trash produced with an increase in the number of inhabitants.
C. There is a correlation between number of inhabitants and amount of trash produced. There may or may not be causation. Further studies would have to be done to determine this.
Answer:
C.
Step-by-step explanation:
There's no problem for now but it still needs to be monitored in case something might happen.
Fatoumata observes marble travel along a horizontal path at a constant rate. The marble travels 1/12 of the length of the path in 4 2/3 seconds. At that rate, how many seconds does it take the object to travel the full length?
A popular soft drink is sold in 2-liter (2,000-milliliter) bottles. Because of variation in the filling process, bottles have a mean of 2,000 milliliters and a standard deviation of 20, normally distributed. a. If the process overfills the bottle by more than 50 milliliters, the overflow will cause a machine malfunction. What is the probability of this occurring
Answer:
0.0062 = 0.62% probability of this occurring
Step-by-step explanation:
When the distribution is normal, we use 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.
In this question, we have that:
[tex]\mu = 2000, \sigma = 20[/tex]
a. If the process overfills the bottle by more than 50 milliliters, the overflow will cause a machine malfunction. What is the probability of this occurring
Probability of filling the bottle with more than 2000 + 50 = 2050 milliliters, which is 1 subtracted by the pvalue of Z when X = 2050. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{2050 - 2000}{20}[/tex]
[tex]Z = 2.5[/tex]
[tex]Z = 2.5[/tex] has a pvalue of 0.9938
1 - 0.9938 = 0.0062
0.0062 = 0.62% probability of this occurring
The circumference of a circle is 14 pi ft. Find its diameter, in feet
Answer:
14
Step-by-step explanation:
Please let me know if you want me to add an explanation as to why this is the answer/how I got this answer. I can definitely do that, I just wouldn’t want to write it if you don’t want me to :)
Answer:
The formula for area of a circle is:
A
=
π
r
2
, where
A
=
area,
π
=
22
7
, and
r
=
radius.
Since we know that the radius is half the diameter of a circle, we know that the radius of the given circle is
14
2
=
7
f
t
.
Hence:
A
=
π
r
2
A
=
22
7
×
7
2
A
=
22
7
×
7
×
7
A
=
22
7
×
7
×
7
A
=
22
×
7
A
=
154
8. Put these numbers into least to greatest order: 8/10, 0.08, 81%, 0.7
ANSWER
0.08 then 0.7 then 8/10 then 81%
Explanation
im going to put everything into fraction because i think it would be easier for u to understand
8/10 > 80/100
0.08> as a fraction is > 8/100
81% as a fraction is 81/100
and last but not least, 0.7 as a fraction is 70/100
so order these from least to greatest
8/100 then 70/100 then 80/100 and then 81/100.
so it would be
0.08 then 0.7 then 8/10 then 81%
^is ur answer
hope this helps.
:)
5 star and brainliest please?
There were 26 students in the classroom. 14 of the students went to the cafeteria and the rest went to the gym. What percentage of students went to the cafeteria?
Answer:
About 53% percent of the students went to the cafeteria.
Step-by-step explanation:
there are 26 students and 14 left that can be put into the fraction 14/26.
To find the percentage you then divide 14 by 26 and turn it into a percent and you get something like 53.846... but you can simplify it to 53%
Answer
54
Step-by-step explanation:
The weight of an object on the moon is 1/6 its weight on earth. If a bowling ball weighs 12 and 1/2 pounds on earth, how much does it weigh on the moon?
A nutritionist would like to estimate the number of times adults exercise each week. To collect information, the nutritionist emails the members of the local fitness center. Which of the following describes the bias that may arise from the results?
A- This is a convenience sample and likely overestimates the frequency of exercise.
B- This is a convenience and likely underestimated the frequency of exercise.
C- This is a voluntary response sample and likely overestimates the frequency of exercise.
D- This is a voluntary response sample and likely underestimates the frequency of exercise.
Answer:
This is a voluntary response sample and likely overestimates the frequency of exercise.
Step-by-step explanation:
I just took the unit test review. The people taking the survey took it voluntarily and it overestimates exercise because it was offered to gym members.
The statement describes the bias that may arise from the results is "This is a voluntary response sample and likely overestimates the frequency of exercise".
Given that,
A nutritionist would like to estimate the number of times adults exercise each week.
To collect information, the nutritionist emails the members of the local fitness center.
We have to determine,
Which of the following describes the bias that may arise from the results?
According to the question,
A nutritionist would like to estimate the number of times adults exercise each week.
To collect information, the nutritionist emails the members of the local fitness center.
The people taking the survey took it voluntarily and it overestimates exercise because it was offered to gym members.
Hence, This is a voluntary response sample and likely overestimates the frequency of exercise.
To know more about Reasoning click the link given below.
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Which graph represents a function?
25% of 200. Find the percentage of the number
Answer:
50
Step-by-step explanation:
0.25 * 200 = 50
25% of 200 is 50
Answer:
50
Step-by-step explanation:
25% of 100 is 25 so add another 100 so u have to add 25
John estimates that there is 150 people at the party . After counting, there are actually 148 at the people . Fine the percent error
Answer:
Step-by-step explanation:
The estimate was off by 2 people. The error was thus -2/148, or about 1%.
21+15a distributive property equavilent expression
PLEASE ANSWER ASAP !!!!!!!!!!!!!!!!!!! WILL GET BRAINLEST IF CORRECT!!!!!!!!!!!!!!!!!!!!!!
Answer:
55 degrees
Step-by-step explanation:
Zack and Noah jogged 2/5 of a mile and walked another 1/4 of a mile. How far did they go in all?
10 ways to divide 96 into equal groups
Answer:
Step-by-step explanation:
48+48=96
32+32+32=96
24+24+24+24=96
12+12+12+12+12+12+12+12=96
6+6+6+6+6+6+6+6+6+6+6+6+6+6+6+6=96
I'm not going to write out the rest of the numbers. I'll multiply them.
4 x 24=96 (etc. 4+4+4....)
3 x 32=96 (etc. 3+3+3....)
2 x 48=96 (etc. 2+2+2....)
1 x 96=96 (etc. 1+1+1....)
I hope this is what you meant. If you liked, mark me Brainliest please.
The number 96 is divided into equal groups, then the number of 10 ways is shown below.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
PEMDAS rule means the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
48 + 48 = 96
32 + 32 + 32 = 96
24 + 24 + 24 + 24 = 96
12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 = 96
6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 = 96
And the rest are written in the form of multiplication. Then we have
4 x 24 = 96 (etc. 4 + 4 + 4 ....)
3 x 32 = 96 (etc. 3 + 3 + 3 ....)
2 x 48 = 96 (etc. 2 + 2 + 2 ....)
1 x 96 = 96 (etc. 1 + 1 + 1 ....)
More about the Algebra link is given below.
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A line that includes the points (-9,-5) and (-10, j) has a slope of -10. What is the value of J
Answer:
j = -15
Step-by-step explanation:
Given that,
A line that includes the points (-9,-5) and (-10, j) has a slope of -10.
The slope of a line for which two points are given is :
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}\\\\-10=\dfrac{j-(-5)}{-10-(-9)}\\\\10=\dfrac{j+5}{-10+9}\\\\10=\dfrac{j+5}{-1}\\\\-10=j+5\\\\j=-10-5\\\\j=-15[/tex]
So, the value of j is equal to -15.
GEOMETRY Find the perimeter of the regular polygon.
3(x - 1)
5x - 6
Answer:
7.5
Step-by-step explanation:
The perimeter of the regular pentagon will be 7.5 units.
What is the perimeter of the regular polygon?All the sides of the regular polygon are congruent to each other. The perimeter of the regular polygon of n sides will be the product of the number of the side and the side length of the regular polygon.
P = (Side length) x n
The sides of the regular polygon are 3(x - 1) and (5x - 6). Then the value of the variable x will be
3(x - 1) = 5x - 6
3x - 3 = 5x - 6
2x = 3
x = 1.5
Then the side length of the regular pentagon will be
Side = 3(1.5 - 3)
Side = 3 (0.5)
Side = 1.5
Then the perimeter of the regular pentagon will be
P = 5 x 1.5
P = 7.5 units
The perimeter of the regular pentagon will be 7.5 units.
More about the perimeter of the regular polygon link is given below.
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a. Miss Butler made a circle graph to show the grades on the term papers. There were 14 B's, 10 A's, and 8 C's.
Awnser All 4 boxes pls
-_- 1x2 3x4 2 3d 34rs 4543 3456