Answer:
a) 0.4772 = 47.72% probability that the average is between 1,142 and 1,150.
b) 0.0228 = 2.28% probability that the average is greater than 1,158.
c) 0 = 0% probability that the average is less than 950.
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.
A certain type of automobile battery is known to last an average of 1,150 days with a standard deviation of 40 days.
This means that [tex]\mu = 1150, \sigma = 40[/tex]
Sample of 100:
This means that [tex]n = 100, s = \frac{40}{\sqrt{100}} = 4[/tex]
(a) The average is between 1,142 and 1,150.
This is the pvalue of Z when X = 1150 subtracted by the pvalue of Z when X = 1142. So
X = 1150
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{1150 - 1150}{4}[/tex]
[tex]Z = 0[/tex]
[tex]Z = 0[/tex] has a pvalue of 0.5
X = 1142
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{1142 - 1150}{4}[/tex]
[tex]Z = -2[/tex]
[tex]Z = -2[/tex] has a pvalue of 0.0228
0.5 - 0.0228 = 0.4772
0.4772 = 47.72% probability that the average is between 1,142 and 1,150.
(b) The average is greater than 1,158.
This is 1 subtracted by the pvalue of Z when X = 1158. So
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{1158 - 1150}{4}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a pvalue of 0.9772
1 - 0.9772 = 0.0228
0.0228 = 2.28% probability that the average is greater than 1,158.
(c) The average is less than 950.
This is the pvalue of Z when X = 950. So
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{950 - 1150}{4}[/tex]
[tex]Z = -50[/tex]
[tex]Z = -50[/tex] has a pvalue of 0
0 = 0% probability that the average is less than 950.
Help please this is for an important test
A cup on the teacher's desk contains 12 pens. There are 3 pens with blue ink and 9 pens with black ink. One student at a time selects a pen at random to sign the attendance sheet and then puts the pen back in the cup.
What is the probability that the first three students all randomly select a pen with blue ink?
A. 1/4
B. 1/27
C. 1/64
D. 1/220
We have 12 pens in total
P(first three pens are blue with replacement) = 3/12 * 3/12 * 3/12 =
(1/4) * (1/4) * (1/4) =
1/ 64
The required probability that the first three students all randomly select a pen with blue ink is 1/64. option C is correct.
Given that,
A cup on the teacher's desk contains 12 pens. There are 3 pens with blue ink and 9 pens with black ink. One student at a time selects a pen at random to sign the attendance sheet and then puts the pen back in the cup.
Probability can be defined as the ratio of favorable outcomes to the total number of events.
Here,
Total number of sample = 12
Favorable outcome = 3
Required probability that the first three students all randomly select a pen with blue ink = 3 / 12 × 3 / 12 × 3 / 12
= 1 / 64
Thus, the required probability that the first three students all randomly select a pen with blue ink is 1/64. option C is correct.
Learn more about probability here:
brainly.com/question/14290572
#SPJ5
A large popcorn bag holds four times as much as a small popcorn bag. At the end of a party,
3 1/3 small bags and 2 1/4 large bags were left.
a) How many small bags would the leftover popcorn fill?
b) How many large bags would the leftover popcorn fill?
Please help me fast, also show all work and steps please:)
Answer:
A] 37 / 3 = 12 1/3 ; B] 37 / 12 = 3 1/12
Step-by-step explanation:
Let small popcorn bag hold = p units popcorn. So, large popcorn bag hold 4 times ie 4p units popcorn.
Left popcorn = 3 1/3 ie 10 / 3 small bags , & 2 1/4 ie 9 / 4 large bags.
So, total popcorn left = Sum( No. of popcorn in each bag x no of bags) = [ 10 p / 3 ] + [ (9 x 4) p / 4 ] = 10p / 3 + 9p = (10p + 27p) / 3 = 37p / 3
A] Small bags for left popcorn = Total left popcorn / Per small bag popcorn = ( 37p / 3 ) / (p) = 37 / 3 = 12 1/3
B] Large bags for left popcorn = Total left popcorn / Per large bag popcorn = ( 37p / 3 ) / (4p) = 37 / 12 = 3 1/12
Using the letters suggested, construct a simple formula:
A car travels a km/h for b km and makes another journey at c km/h for d km.
a. Find the total distance (s km) the car travels
b. Find the formula for the Average Speed of the entire journey.
Answer:
Speed = distance / time
Time = distance/ Speed
Distance = Speed x time
Which table represents a function
Answer:
A
Step-by-step explanation:
because it passes the vertical line test and also for every x, there is only one y
Order these numbers from least to greatest: 5, 0, 1, -13 -1-1
Answer:
-1 1/2, -1, 0, 1/2, 1
Step-by-step explanation:
Can someone please help me it’s urgent
Answer:
8.5 in
Step-by-step explanation:
You are solving for the hypotenuse right? So you would use this formula:
c = square root a^2+b^2
the c is the hypotenuse (long side of a right triangle) and a will be 4 and b will be 7.5. substitute the numbers in, solve, and you get 8.5 inches!
x = square root 4^2 + 7.5^2
x = square root 16 + 56.25
x = square root 72.25
x = 8.5 inches
Given F(x) = 3x-2 and G(x) = 4-x2. Evaluate 2F(1) - 3G(3).
Answer:
[tex]9x^{2} -34[/tex]
Step-by-step explanation:
Use the given functions to set up and simplify [tex]2F(1)-3G.3.[/tex]
The point in the middle between 3G and 3 is a multiplication sign btw
if A(2;2) and B(-3;4), determine the equation of AB, in the form y=mx+c
Answer:
[tex]y = -\frac{2}{5}x + \frac{14}{5}[/tex]
Step-by-step explanation:
Equation of a line:
The equation of a line has the following format:
[tex]y = mx + c[/tex]
In which m is the slope and c is the y-intercept(value of y when x = 0).
A(2;2) and B(-3;4)
When we have two points, the slope is the change in y divided by the change in x. So
Change in y: 4 - 2 = 2
Change in x: -3 - 2 = -5
Slope: [tex]m = \frac{2}{-5} = -\frac{2}{5}[/tex]
So
[tex]y = -\frac{2}{5}x + c[/tex]
A(2;2)
When [tex]x = 2, y = 2[/tex]. We use this to find c.
[tex]y = -\frac{2}{5}x + c[/tex]
[tex]2 = -\frac{2}{5}(2) + c[/tex]
[tex]c = 2 + \frac{4}{5} = \frac{10}{5} + \frac{4}{5} = \frac{14}{5}[/tex]
So
[tex]y = -\frac{2}{5}x + \frac{14}{5}[/tex]
I need help ASAP!!!!!! Calculate the slope of the line through the points (-1, 1) and (4, 0).
A. 5x
B.-1/5
C.1/5
D.-5
Answer:
B. -1/5
Step-by-step explanation:
To find the slope we place (0-1) over (4- (-1))
HELP CAN SOMEONE TELL ME THE ANSWER I CANT GET A BAD GRADE.
Answer:
34.1cm^2
Step-by-step explanation:
Area of triangle = 1/2 x base x height
=1/2 x6.2 x11
=34.1cm^2
13 - [(3² x 4) - 30]
Answer:
7
Step-by-step explanation:
13 - [(3² x 4) - 30]
13 - [(9 x 4) - 30]
13 - (36 - 30)
13-6
7
Answer:
7
Step-by-step explanation:
I think the answer you're looking for is 7
the model shows -3x + 5 + 2x - 1. what value of x makes the equation true?
a. x = -6
b. x= 4
c. x = -4
d. x= 6
please help. 30 points
Answer:
hopes this helps
Step-by-step explanation:
B -x+4
(-8,3)(-3,-4.5) what is zero of g?
Answer:
the daimeter of the heart of the heart of the heart
help plssssssssssssssssss
Answer:
There’s two options for each. Look below.
Step-by-step explanation:
Savings: there is no risk of losing any money put into this account
interest income is the only way to earn money in this type
‘investment: this account may generate income from a variety of sourses.
If no deposits or withdrawals are made, money held in this acct..
How many solutions
Line A: x + y = 2
Line B: 2x + y = 4
Answer:
1 solution (2, 0 )
Step-by-step explanation:
Given the 2 equations
x + y = 2 → (1)
2x + y = 4 → (2)
Subtract (1) from (2) term by term to eliminate y
2x - x + y - y = 4 - 2 , that is
x + 0 = 2
x = 2
Substitute x = 2 into either of the 2 equations and evaluate for y
Substituting into (1)
2 + y = 2 ( subtract 2 from both sides )
y = 0
one solution is (2, 0 )
unction f(x) = (x − 4)(x − 2) is shown. On a coordinate plane, a parabola opens up. It goes through (2, 0), has a vertex at (3, negative 1), and goes through (4, 0). What is the range of the function? all real numbers less than or equal to 3 all real numbers less than or equal to −1 all real numbers greater than or equal to 3 all
9514 1404 393
Answer:
(d) all real numbers greater than or equal to -1
Step-by-step explanation:
The y-value of the vertex at (3, -1) is the minimum of the function. All y-values equal to or greater than -1 are in the range of the function.
y ≥ -1
how can we rewrite the slope formula,so that we have point-slope form
Is it possible for a triangle to have a 54 degree angle and a 126 degree angle? Explain why or why not.
Answer:
No
Step-by-step explanation:
Those are only 2 angles and they already equal 180, Every single triangle has a sum of 180 and if you already hit 180 with only 2 out of the 3 points, it's not possible
Answer:
No
Step-by-step explanation:
No, because the 3 angles of a triangle have to add up to 180 degrees. The given 2 angles already add up to 180 degrees leaving no room for the missing angle.
For the given configuration, determine how many different licence plates are possible of (a) digits and letters can be repeated, and (b) digits and letters cannot be repeated. NO LINKS!!
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Answer:
5a,b = 17,576,000; 11,232,000
6. 45,697,600; 32,292,000
7. 6,760,000; 3,276,000
8. 118,813,760; 78,936,000
Step-by-step explanation:
The number of possible ways the characters can occur is the product of the numbers of ways a character can be selected in each position. If letters or digits cannot repeat, the number of possible selections is reduced by 1 in each new location.
5a. 26×26×26×10×10×10 = 26³×10³ = 17,576,000
5b. 26×25×24×10×9×8 = 11,232,000
__
6a. 10²×26⁴ = 45,697,600
6b. 10×9×26×25×24×23 = 32,292,000
__
7a. 10⁴×26² = 6,760,000
7b. 10×9×8×7×26×25 = 3,276,000
__
8a. 26⁵×10 = 118,813,760
8b. 26×25×24×23×22×10 = 78,936,000
49°
Solve for 42.
2 = [?]
44/62
Answer:
∠2 = 41°
Step-by-step explanation:
∠2 + 49° + 90° = 180°
∠2 + 139° = 180°
∠2 = 180° - 139°
∠2 = 41°
Answer:
[tex] \displaystyle \angle2 = \bigg[{41}^{ \circ} \bigg][/tex]
Step-by-step explanation:
we are given a right angle triangle
we want to figure out the missing interior angle
recall that,
one of angle measure of a right angle triangle is 90° interior angles of a triangle add up to 180°thus our equation is
[tex] \displaystyle {49}^{ \circ} + \angle2 + {90}^{ \circ} = {180}^{ \circ} [/tex]
simplify addition:
[tex] \displaystyle \angle2 + {139}^{ \circ} = {180}^{ \circ} [/tex]
cancel 139° from both sides:
[tex] \displaystyle \angle2 = {41}^{ \circ} [/tex]
hence,
the measure of the missing angle is 41°
Simplify 5 (x + 2) + 2 (x - 5)
Answer: 7x let me know if you need an explantion.
Write a equation to represent the hanger ,7th grade math help me
(100 POINTS WILL MARK BRAINLIEST FOR ACTUAL ANWSERS) Write an equation in standard form of the ellipse with vertices (0,-2) and (8,-2), and a focus located at (7,-2)
Answer:
(x-4)^2 / 16 + (y+2)^2 / 7 = 1 or 7x^2-56x+16y^2+64y+64=0
Step-by-step explanation:
Either one should be right I think. Hope this helps.
Help, I need this as quick as possible
Answer:
multiply the top number by 4 also and what ever answer you get by doing 24×4 place that number over 100 and that number will be your percentage
Item 2
Jake ran 145 meters before lunch and 389 meters after lunch.
How many kilometers did Jake run in all?
A. 0.00534 km
B. 0.0534 km
C. 0.534 km
D. 5.34 km
Please help me I've been on this question for like and hour-
Answer:im so sorry i dont know this one
Step-by-step explanation:but i would try adding subtracting or divison
Answer:
21
Step-by-step explanation:
We can use a proportion to solve this problem
8 : 33.6 = 5 : OP
OP = (33.6 x 5)/8 = 21
¿Cuál de las siguientes respuestas es equivalente a 5 km?
(3 puntos)
50.000 metros
500 metros
5.000 metros
0.005 metros
Answer:
5
[tex] 5 \times 100 = 500[/tex]
Mathematics
10³x10³x10²
Answer:
100,000,000/10^8
Step-by-step explanation:
10^3 = 1000
10^3 = 1000
10^2 = 100
Therefore,
= (1000) x (1000) x (100)
= (100,000) x (100)
= 100,000,000
or
= 10^8
Can somebody help, will give brainliest
9514 1404 393
Answer:
c = 2segments 10, 8, 6 (top down)Step-by-step explanation:
The sum of top and bottom bases is twice the midsegment.
(c² +6) +(c² +2) = 2(4c)
2c² -8c +8 = 0 . . . . . . . . . subtract 8c
2(c -2)² = 0 . . . . . . . . factor
c = 2 . . . . . . the value that makes the binomial be zero
The value of c is 2; the segment lengths (top-down) are 10, 8, 6.
Question 1
Simplify the following arithmetic expression without using a calculator:
1/2 + 7/8 X 49/8 = 7/2 - 3/32
12-1/2 x 271/2
Answer:
0 = 0 = 0 = 0 = 0 < 1/
2
< 7/
8
< 7/
2
< 49/
8
< 12 < 271/
2
0 is equal to 0 is equal to 0 is equal to 0 is equal to 0 is less than 1/
2
is less than 7/
8
is less than 7/
2
is less than 49/
8
is less than 12 is less than 271/
2
0/
8
= 0/
8
= 0/
8
= 0/
8
= 0/
8
< 4/
8
< 7/
8
< 28/
8
< 49/
8
< 96/
8
< 1084/
8
Step-by-step explanation: