(CO 3) The weights of ice cream cartons are normally distributed with a mean weight of 20.1 ounces and a standard deviation of 0
.3 ounces. You randomly select 25 cartons. What is the probability that their mean weight is greater than 20.06 ounces? 0.553 0.748 0.252 0.447
1 answer:
Answer:
The probability is 0.252 ⇒ 3rd answer
Step-by-step explanation:
* Lets revise how to find the z-score
- The rule the z-score is z = (M - μ)/σM , where
# M is the sample mean
# μ is the mean
# σM is the standard deviation of the sample mean (standard error)
- The rule of σM = σ/√n , where n is the sample size
* Lets solve the problem
∵ The mean weight is 20.1 ounces
∴ μ = 20.1
∵ The standard deviation is 0.3 ounces
∴ σ = 0.3
∵ You randomly select 25 cartons
∴ n = 25
∵ Their mean weight is greater than 20.06
∴ M = 20.06
- Lets find σM
∵ σM = σ/√n
∴ σM = 0.3/√25 = 0.3/5 = 0.06
- Lets find z-score
∵ z-score = (M - μ)/σM
∴ z-score = (20.06 - 20.1)/0.06 = -0.04/0.06 = - 0.6670
- To find P(M > 20.06) you will asking to find the proportion of area
under the standard normal distribution curve for all z-scores > -0.670
- It can be read from a z-score table by referencing a z-score of -0.670
- Look to the attached table
∴ P(M > 20.06) = 0.2514
* The probability is 0.252
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Problem 1)
AC is only perpendicular to EF if angle ADE is 90 degrees
(angle ADE) + (angle DAE) + (angle AED) = 180
(angle ADE) + (44) + (48) = 180
(angle ADE) + 92 = 180
(angle ADE) + 92 - 92 = 180 - 92
angle ADE = 88
Since angle ADE is actually 88 degrees, we do NOT have a right angle so we do NOT have a right triangle
Triangle AED is acute (all 3 angles are less than 90 degrees)
So because angle ADE is NOT 90 degrees, this means AC is NOT perpendicular to EF
-------------------------------------------------------------
Problem 2)
a) The center is (2,-3)
The center is (h,k) and we can see that h = 2 and k = -3. It might help to write (x-2)^2+(y+3)^2 = 9 into (x-2)^2+(y-(-3))^2 = 3^3 then compare it to (x-h)^2 + (y-k)^2 = r^2
---------------------
b) The radius is 3 and the diameter is 6
From part a), we have (x-2)^2+(y-(-3))^2 = 3^3 matching (x-h)^2 + (y-k)^2 = r^2
where
h = 2
k = -3
r = 3
so, radius = r = 3
diameter = d = 2*r = 2*3 = 6
---------------------
c) The graph is shown in the image attachment. It is a circle with center point C = (2,-3) and radius r = 3.
Some points on the circle are
A = (2, 0)
B = (5, -3)
D = (2, -6)
E = (-1, -3)
Note how the distance from the center C to some point on the circle, say point B, is 3 units. In other words segment BC = 3.
AC is only perpendicular to EF if angle ADE is 90 degrees
(angle ADE) + (angle DAE) + (angle AED) = 180
(angle ADE) + (44) + (48) = 180
(angle ADE) + 92 = 180
(angle ADE) + 92 - 92 = 180 - 92
angle ADE = 88
Since angle ADE is actually 88 degrees, we do NOT have a right angle so we do NOT have a right triangle
Triangle AED is acute (all 3 angles are less than 90 degrees)
So because angle ADE is NOT 90 degrees, this means AC is NOT perpendicular to EF
-------------------------------------------------------------
Problem 2)
a) The center is (2,-3)
The center is (h,k) and we can see that h = 2 and k = -3. It might help to write (x-2)^2+(y+3)^2 = 9 into (x-2)^2+(y-(-3))^2 = 3^3 then compare it to (x-h)^2 + (y-k)^2 = r^2
---------------------
b) The radius is 3 and the diameter is 6
From part a), we have (x-2)^2+(y-(-3))^2 = 3^3 matching (x-h)^2 + (y-k)^2 = r^2
where
h = 2
k = -3
r = 3
so, radius = r = 3
diameter = d = 2*r = 2*3 = 6
---------------------
c) The graph is shown in the image attachment. It is a circle with center point C = (2,-3) and radius r = 3.
Some points on the circle are
A = (2, 0)
B = (5, -3)
D = (2, -6)
E = (-1, -3)
Note how the distance from the center C to some point on the circle, say point B, is 3 units. In other words segment BC = 3.
Answer: 6 tablets.
<h3>Step-by-step explanation:-</h3>Given:
• A certain medication is available only in 400 μg tablets.
So, in milligrams :- 0.4 mg
• It is also given that the patient needs to take 2.4 mg per day.
Solution:
So, in order to know how many tablets she should take, please do as following:-
Hence, she must take <u>6 tablets per day</u>.
✍️ <em>By </em><em>Benjemin</em> ☺️