a normal distribution has a mean of 56 and a standard deviation of 8. Find the percentage of data values that are in the given interval. Use the curve to aid you.
Answers
Answer:
12) Between 40 and 64 = 0.815
13) Between 32 and 40 = 0.0235
14) Between 56 and 64 = 0.34
15) At most 56 = 0.515
16) At least 72 = 0.025
17) At most 64 = 0.855
Explanation:
To answer this, we will convert each of the values into their standardized form to make this easier.
The standardized score for any value is the value minus the mean then divided by the standard deviation.
z = (x - μ)/σ
x = Each value
μ = Mean = 56
σ = Standard deviation = 8
12) Between 40 and 64
For 40,
z = (x - μ)/σ = (40 - 56)/8 = (-16/8) = -2
For 64
z = (x - μ)/σ = (64 - 56)/8 = (8/8) = 1
So,
Between 40 and 64 = Between -2 and 1
From the curve, noting that the central point is the mean, with standard score of 0, the lines before it move in step of 1 standard deviation towards the negative side, that is, -1, -2, etc. And the lines before the central point move towards the positive side, that is, 1, 2, 3, etc.
So,
Between -2 and 1 = 0.135 + 0.34 + 0.34 = 0.815
13) Between 32 and 40
For 32,
z = (x - μ)/σ = (32 - 56)/8 = (-24/8) = -3
For 40,
z = (x - μ)/σ = (40 - 56)/8 = (-16/8) = -2
So,
Between 32 and 40 = Between -3 and -2 = 0.0235
14) Between 56 and 64
For 56,
z = (x - μ)/σ = (56 - 56)/8 = (0/8) = 0
For 64,
z = (x - μ)/σ = (64 - 56)/8 = (8/8) = 1
Between 56 and 64 = Between 0 and 1 = 0.34
15) At most 56
For 56,
z = (x - μ)/σ = (56 - 56)/8 = (0/8) = 0
At most 56 = At most 0 = 0.0015 + 0.0235 + 0.15 + 0.34 = 0.515
All the regions before z = 0)
16) At least 72
For 72,
z = (x - μ)/σ = (72 - 56)/8 = (16/8) = 2
At least 72 = At least 2 = 0.0235 + 0.0015 = 0.025
(All the regions from z = 2 to the end)
17) At most 64
For 64,
z = (x - μ)/σ = (64 - 56)/8 = (8/8) = 1
At most 64 = At most 1 = 0.0015 + 0.0235 + 0.15 + 0.34 + 0.34 = 0.855
(All the regions before z = 1)
Hope this Helps!!!
Related Questions
please help :) thanks !
Answers
Answer:
Step-by-step explanation:
b
Ms. Wright looks at the menu in a restaurant. She wants to order a bowl of salad priced at $13.10 and a glass of fruit juice priced at $5.90. There are a 5% sales tax and a 3% meals tax on all food and beverages. Is she able to pay for her meal with $20? Explain your reasoning.
Answers
Answer:
No
Step-by-step explanation:
No, she is not able to pay for her meal with 20 dollars. The first step to solve this problem is to add up 13.10 and 5.90 so you can see how much money Ms. Wright has to spend on the food and drinks alone. 13.10 + 5.90 is 19. Since there are 5% and 3% of taxes on all food and beverages, there is 8% in total of taxes. 8% of 19 is 1.52. 19 plus 1.52 is 20.52 which is greater than 20. Therefore, Ms. Wright cannot pay for her meal with 20 dollars.
Trevor is interested in purchasing the local hardware/electronic goods store in a small town in South Ohio. After examining accounting records for the past several years, he found that the store has been grossing over $850 per day about 60% of the business days it is open. Estimate the probability that the store will gross over $850
Answers
This question is incomplete, the complete question is;
Trevor is interested in purchasing the local hardware/electronic goods store in a small town in South Ohio. After examining accounting records for the past several years, he found that the store has been grossing over $850 per day about 60% of the business days it is open. Estimate the probability that the store will gross over $850 at least 6 out of 10 business day
Answer:
P( at least 6 out of 10 business days ) = 0.6312
Step-by-step explanation:
Given the data in the question;
p = 60% = 0.6
q = 1 - p = 1 - 0.6 = 0.4
Using Binomial distribution;
P( X = r ) = [tex]^nC_r p^rq^{n-r[/tex]
where [tex]^nC_r = n!/(r!(n-r))[/tex]
we substitute
P( at leas 6 ) = P(6) + P(7) + P(8) + P(9) + P(10)
= [¹⁰C₆ × 0.6⁶ × 0.4⁴] + [¹⁰C₇ × 0.6⁷ × 0.4³] + [¹⁰C₈ × 0.6⁸ × 0.4²] + [¹⁰C₉ × 0.6⁹ × 0.4¹] + [¹⁰C₁₀ × 0.6¹⁰ × 0.4⁰]
= [0.250] + [0.214] + [0.1209] + [ 0.0403] + [ 0.00604 ]
= 0.6312
Therefore, P( at least 6 out of 10 business days ) = 0.6312
For every 5 pounds of tomatoes ordered, the restaurant orders 9 pounds of onions. If Everly orders
108 pounds of onions, how many pounds of tomatoes will she need to order?
Type or write your answers in the box below.
Answers
Answer:
[tex]\left[ 60- pounds][/tex]
Step-by-step explanation:
Ratio of tomatoes to onions = 5:9
so now it will be
5x: 108
we can solve it by doing this
x = 108/9
x = 12
so we multiply
5*x = 5x
5*12 = 60
She would need 60 pounds
We can do this
x=12
So we have to multiply to find the answer
5*x= 5x
5*12=60
Pls help asap!!!!!!!!!!!!!!
Answers
One card is randomly selected from a deck of cards. Find the odds:
in favor of getting a spade.
Answers
Answer:
1/4 chance or 0.25 or 25%
Step-by-step explanation:
One forth of cards in a deck are spades
Answer:
1/4
Step-by-step explanation:
In a deck of cards, there are 52 cards (not including jokers)
and there are 13 cards that are spades, so it's simply just 13/52 which simplifies to 1/4
help pleaseee, this is for math class
Answers
Answer:
Step-by-step explanation:
3h = 3×7, not 37.
3h + 13 = 3×7 + 13 = 34
A total surface area is _ square inches
Answers
80% of c is 20. What is c ?
Answers
Answer:
25
Step-by-step explanation:
Mel has 1/2 gallon of milk in the refrigerator. He drinks 1/4 of the milk. How much milk does Mel drink?
Answers
Answer:
1/3
Step-by-step explanation:
Answer:
3/4
Step-by-step explanation:
The answer is 3/4 because 1/2 can be turned into 2/4 so the denominators are equal and then you add 1/4 and 3/4
2/4=1/2 because they are both a half
Use the description of an experiment done in a children's hospital.
A music therapist was interested in investigating whether listening to music or composing music had an influence on both anxiety levels and oxygen saturation in children who were hospitalized for asthma-related illnesses. Thirty-two children spent 20 minutes listening to classical waltzes played on a piano. On a different day, they spent 20 minutes composing their own short pieces of music using a software program.
When listening to music: For the physiological measure, the critical value for t was larger than the test statistic for the observed data. For the anxiety measure, the critical value for t was smaller than the test statistic for the observed data.
When composing music: For the physiological measure, the critical value for t was larger than the test statistic for the observed data. For the anxiety measure, the critical value for t was larger than the test statistic for the observed data.
When writing the results of the music therapist's study, which of these statements reflects the correct conclusions that should be drawn from the results and then included as part of the interpretation paragraph?Question 8 options:
a) Music therapists should make pediatric asthma patients compose music in order to increase their oxygen saturation.
b) Music therapists should make pediatric asthma patients listen to music in order to reduce their anxiety.
c) Pediatric asthma patients should listen to music in order to increase their oxygen saturation.
d) Additional information is needed to draw a proper conclusion.
Answers
Answer:
d) Additional information is needed to draw a proper conclusion
Step-by-step explanation:
When listening to music;
Physiological measure
Critical t > Test statistic Accept H₀
Anxiety measure
Critical t < Test statistic Reject H₀
When composing music;
Physiological measure
Critical t > Test statistic Accept H₀
Anxiety measure
Critical t > Test statistic Accept H₀
When the test statistic is larger the critical 't' we reject the hypothesis that there is no difference in the observation, and we accept the alternative hypothesis
The test results having a larger critical 't' than the test statistics suggest that there is no difference between physiological and anxiety influence of composing music on pediatric asthma patients
However, given that when listening to music, the critical 't' is lest than the test statistic for the anxiety parameter of the participants, there is sufficient statistical evidence to suggest that there in an influence on the anxiety of pediatric asthma patients when they listen to music, however, it is not stated if the anxiety increases or decreases, therefore additional information is needed
The number of calories in fruit smoothies varies from brand to brand. The population distribution of calories is strongly skewed to the right. The central limit theorem says that:___________
a. the average calorie count of a large number of fruit smoothie brands has a sampling distribution that is exactly Normal.
b. the average calorie count of a large number of fruit smoothie brands has a sampling distribution that is close to Normal.
c. as the number of brands of fruit smoothies increases, their average calorie count gets ever closer to the mean μ for all fruit smoothies of this type.
d. the average amount of calories of a large number of fruit smoothie brands has a sampling distribution with the same shape (strongly skewed) as the population distribution.
e. the average calorie count of a large number of fruit smoothie brands has a sampling distribution with a similar shape but not as extreme (skewed, but not as strongly) as the population distribution.
Answers
Answer:
b. the average calorie count of a large number of fruit smoothie brands has a sampling distribution that is close to Normal.
Step-by-step explanation:
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.
Applying to this question:
The distribution of the number of calories in fruit smoothies is strongly skewed to the right. However, in a sample with a large number of fruit smoothies, the sampling distribution will be approximately normal, so the correct answer is given by option B.
Answer:
B
Step-by-step explanation:
Help me with this geometry question!!
Answers
Answer:
A) trapezoid a=141 b=69
Step-by-step explanation:
It must be a trapezoid because two of the sids are not parallel. The interior angles of any quadrilateral must equal 360, and each side of a trapezoid must equal 180, so:
A) trapezoid a=141 b=69
Answer:
a
Step-by-step explanation:
You move right 3 units. You end at (5, 2). Where did you start?
Answers
Answer:
8,2
Step-by-step explanation:
You started at (2,2)
EXPLANATION:
you subtract the 5 by 3 because moving to the right affects the x axis, and (x,y), so the 5 is what is being affected
How many square feet of outdoor carpet will
we need for this hole?
Answers
Find the perimeter of the figure. due today
Answers
Answer:
62
Step-by-step explanation:
Since you are simply finding the perimeter, I assume they just want you to add all the sides. 13 + 15 + 10 + 10 + 14 = 62
what is the slope of the line.
Answers
Answer:
m=3/2 or m=1.5
Step-by-step explanation:
slope formula:
m=(y1-y2)/(x1-x2)
in order to get this we need two points such as (3,0) and (1,-3) which are points on this line. So:
m=(0-(-3))/(3-1)
m=3/2 or m=1.5
the following list contains the number of movies That a group of 8 students saw in theaters in the past 12 months.
7,11,14,6,16,11,11,18
Find the median number of movies that the students saw.
Answers
Answer:
I'm pretty sure its 11
first orginize the numbers in numerical order
second the medj an is the middle numbe, if they are to find the mean of those two only
PLEASE PLEASE PLEASEEEEE HELP!!!!!!!!!
Answers
Ratio of area= (scale factor)^2 : 1 = (3/2)^2 : 1 = 9/4 : 1
Ratio of volume = (scale factor)^3 : 1 = (3/2)^3 : 1 = 27/8 : 1
i dont understand what im doing wrong
Answers
Answer:
8
Step-by-step explanation:
-2 x -2 = 4
4 - (-28 / 7 = -4)
4- -4 = 8
6(2b+5)=12b×30
What did Joseph do wrong and whats the correct answer
Answers
Answer:
he placed a * sign instead of an add sign in the second part of the equation
Step-by-step explanation:
6(2b+5)=6*2b + 6*5 = 12b + 30
Amir thinks of a number,
He triples it and adds 9 to get 54.
What number did he think of?
Answers
Answer:
The number he think of is 15
Step-by-step explanation:
Let x be the number
3x + 9 = 54
x = (54-9) / 3
x = 15
The number he think of is 15
Answer:
15
Step-by-step explanation:
3x + 9 = 54
x = (54-9) / 3
x = 15
what is 64/7 simplified?
Answers
Answer:
9 1/7
Step-by-step explanation:
This is the answer because 64 divided by 7 is 9.142... this means that there are 9 whole numbers and 1/7 remaining after the 9 whole numbers
What percent of 84 is 42
Answers
Suppose a home improvement contractor is painting the walls and ceiling of a rectangular room. The volume of the room is 288 cubic feet. The cost of wall paint is $0.06 per square foot and the cost of ceiling paint is $0.16 per square foot. Let x, y, and z be the length, width, and height of a rectangular room respectively. Identify the room dimensions that result in a minimum cost for the paint and use these dimensions to find the minimum cost for the paint. Round your answer to the nearest cent.
Answers
Answer:
The minimum cost is $17.30c
Step-by-step explanation:
Given
[tex]V = 288[/tex] --- Volume
[tex]C_1 = 0.06[/tex] --- cost of wall paint
[tex]C_2 = 0.16[/tex] ---cost of ceiling paint
Required
Minimum cost of paint
The volume is calculated as:
[tex]V =xyz[/tex]
Substitute 288 for V
[tex]288 =xyz[/tex]
Make z the subject
[tex]z = \frac{288}{xy}[/tex]
The surface area is calculated as:
[tex]Area = 2(yz + xz) + xy[/tex]
Because xy represent the dimension of the ceiling and the opposite of the ceiling (the floor) will not be painted. Hence, it does not require a coefficient of 2
The cost is:
[tex]C = 0.06 * 2(yz + xz) + 0.16 * xy[/tex]
Substitute [tex]z = \frac{288}{xy}[/tex]
[tex]C = 0.06 * 2(y*\frac{288}{xy} + x*\frac{288}{xy}) + 0.16 * xy[/tex]
[tex]C = 0.06 * 2(\frac{288}{x} + \frac{288}{y}) + 0.16 * xy[/tex]
[tex]C = 0.12(\frac{288}{x} + \frac{288}{y}) + 0.16 * xy[/tex]
[tex]C = (\frac{34.56}{x} + \frac{34.56}{y}) + 0.16 * xy[/tex]
[tex]C = (\frac{34.56}{x} + \frac{34.56}{y}) + 0.16 xy[/tex]
Differentiate w.r.t x and y
[tex]C_x = -\frac{34.56}{x^2} + 0.16y[/tex]
[tex]C_y = -\frac{34.56}{y^2} + 0.16x[/tex]
By comparison: [tex]x = y[/tex]
Set them equal to 0
[tex]C_y = -\frac{34.56}{y^2} + 0.16x=0[/tex]
[tex]-\frac{34.56}{y^2} + 0.16x=0\\[/tex]
Substitute x for y
[tex]-\frac{34.56}{x^2} + 0.16x=0[/tex]
[tex]0.16x=\frac{34.56}{x^2}[/tex]
Cross multiply
[tex]0.16x^3 = 34.56[/tex]
[tex]x^3 = \frac{34.56}{0.16}[/tex]
[tex]x^3 = 216[/tex]
Take the cube root of both sides
[tex]x = \sqrt[3]{216}[/tex]
[tex]x = 6[/tex]
[tex]x=y= 6[/tex]
Substitute 6 for x and for y in [tex]C = (\frac{34.56}{x} + \frac{34.56}{y}) + 0.16 xy[/tex]
[tex]C = (\frac{34.56}{6} + \frac{34.56}{6}) + 0.16 * 6* 6[/tex]
[tex]C = (\frac{2*34.56}{6}) + 5.76[/tex]
[tex]C = 11.52 + 5.76[/tex]
[tex]C = 17.28[/tex]
[tex]C = 17.3[/tex] --- approximated
Mast
Gabi tried to solve an equation step by step.
Skill
= 80
10
algeb
1
j
· 10 = 80 · 10 Step 1
10
ne-
j = 800
Step 2
Find Gabi's mistake.
ne-
Choose 1 answer:
cual
Answers
Answer:
the answer is c
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
What is the diameter of a 2m circle?
Answers
Answer:
If 2m is the radius, the diameter is 4 meters.
2*2=4
2*2=4
Explanation
The diameter of a circle is the distance from one edge to the other, passing through the center. It is twice the radius.
So the diameter would be 2 cause 2 x 2=4
If set M =[even digits from 2 to 8]. Find n(M)
Answers
Answer:
n(M) = 4
Step-by-step explanation:
M = (2,4,6,8)
n(M) = Number of values in set M.
n(M) = 4
Need help please thanks
Answers
Answer:
6.
Just count the x's on the graph...
Please help me find what ? Is
Answers
Answer:
My answer is 43 its that rigth