Assume the readings on thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. Find the probability that a randomly selected thermometer reads between −2.23 and −1.69 and draw a sketch of the region.
Answers
Answer:
0.0326 = 3.26% probability that a randomly selected thermometer reads between −2.23 and −1.69.
The sketch is drawn at the end.
Step-by-step explanation:
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.
Mean of 0°C and a standard deviation of 1.00°C.
This means that [tex]\mu = 0, \sigma = 1[/tex]
Find the probability that a randomly selected thermometer reads between −2.23 and −1.69
This is the p-value of Z when X = -1.69 subtracted by the p-value of Z when X = -2.23.
X = -1.69
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{-1.69 - 0}{1}[/tex]
[tex]Z = -1.69[/tex]
[tex]Z = -1.69[/tex] has a p-value of 0.0455
X = -2.23
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{-2.23 - 0}{1}[/tex]
[tex]Z = -2.23[/tex]
[tex]Z = -2.23[/tex] has a p-value of 0.0129
0.0455 - 0.0129 = 0.0326
0.0326 = 3.26% probability that a randomly selected thermometer reads between −2.23 and −1.69.
Sketch:
Related Questions
Use the functions below to complete Parts 1 and 2.
f(x)= |x| g(x)= |x+2| - 3
Part 1: Graph f(x) and g(x) on the grid below. Label each graph.
HINT: Making a table of values for each function may help you to graph them.
Part 2: describe how the graph of g(x) relates to the graph of its parent function, f(x).
HINT: Think about how f(x) was shifted to get g(x).
Answers
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Answer:
1. see below
2. g(x) is f(x) translated left 2 and down 3
Step-by-step explanation:
1. The graphs are attached. F(x) is in red; g(x) is in blue.
__
2. The graph of g(x) = f(x -h) +k is the parent function translated by (h, k). Here we have (h, k) = (-2, -3), so g(x) is f(x) translated left 2 and down 3.
Suppose f(x)=x^2. What is the graph of g(x)=1/2f(x)?
Answers
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Answer:
see attached
Step-by-step explanation:
The graph of g(x) is a vertically scaled version of the graph of f(x). The scale factor is 1/2, so vertical height at a given value of x is 1/2 what it is for f(x). This will make the graph appear shorter and fatter than for f(x).
The graph of g(x) is attached.
What is the product?
(-2d^2+5)(5d^2-6s)
Answers
Answer:
= -10d^4 + 12d^2s + 25d^2 - 30s
The number 0 is a critical point of the autonomous differential equation dx/dt = 7xn, where n is a positive integer. For what values of n is 0 asymptotically stable? Semi-stable? Unstable?
Answers
Answer:
a) 0 is stable when n = odd
b) 0 is semi-stable when n = even
c) 0 is unstable when n is odd
Step-by-step explanation:
Th differential equation for this question
dx/dt = x^n
n = positive integer
a) value of n where 0 is stable
0 is stable when x^n is replaced with -x^n
because considering n to be an odd number
-x^n > 0 when x < 0 while -x^n < 0 when x > 0
∴ In this scenerio we can conclude that 0 is stable when n = odd number
b) Value of n where 0 is Semi-stable
assuming n is an even number
x^n > 0 for all the values of x
c) Value of n where 0 is unstable
lets assume n is odd
when n < 0, xⁿ < 0
when n > 0, xⁿ > 0
i.e. 0 is asymptotically unstable when n is an odd number
If he is correct, what is the probability that the mean of a sample of 68 computers would differ from the population mean by less than 2.08 months
Answers
Complete Question
The quality control manager at a computer manufacturing company believes that the mean life of a computer is 91 months with a standard deviation of 10 months if he is correct. what is the probability that the mean of a sample of 68 computers would differ from the population mean by less than 2.08 months? Round your answer to four decimal places. Answer How to enter your answer Tables Keypad
Answer:
[tex]P(-1.72<Z<1.72)=0.9146[/tex]
Step-by-step explanation:
From the question we are told that:
Population mean \mu=91
Sample Mean \=x =2.08
Standard Deviation \sigma=10
Sample size n=68
Generally the Probability that The sample mean would differ from the population mean
P(|\=x-\mu|<2.08)
From Table
[tex]P(|\=x-\mu|<2.08)=P(|z|<1.72)[/tex]
T Test
[tex]Z=\frac{\=x-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]
[tex]Z=\frac{2.08}{\frac{10}{\sqrt{68} } }[/tex]
[tex]Z=1.72[/tex]
[tex]P(|\=x-\mu|<2.08)=P(|z|<1.72)[/tex]
[tex]P(-1.72<Z<1.72)[/tex]
Therefore From Table
[tex]P(-1.72<Z<1.72)=0.9146[/tex]
Determine if the two figures are congruent and explain your answer.
Answers
Explanation: All respective sides have the same slope
The slope of the shapes are congruent.
Left on together, the cold and hot water faucets of a certain bathtub take 4 minutes to fill the tub. If it takes the hot water faucet minutes to fill the tub by itself, how long will it take the cold water faucet to fill the tub on its own?
Do not do any rounding.
Answers
Answer:
[tex]Cold = \frac{1}{6}\ mins[/tex]
Step-by-step explanation:
The correct given parameters are:
[tex]Both = \frac{1}{4}\ mins[/tex]
[tex]Hot = \frac{1}{12}\ mins[/tex]
Required
Time taken by the cold water faucet
We have:
[tex]Cold + Hot = Both[/tex]
Make Cold the subject
[tex]Cold = Both -Hot[/tex]
So, we have:
[tex]Cold = \frac{1}{4}-\frac{1}{12}[/tex]
Take LCM
[tex]Cold = \frac{3-1}{12}[/tex]
[tex]Cold = \frac{2}{12}[/tex]
Divide by 2
[tex]Cold = \frac{1}{6}[/tex]
Write the monomial in its standard form. Name its coefficient and
identify its degree:
2
3
2 mºn :4.573
Answers
Answer:
A monomial in standard form is (essentially) the product of one or more factors: a constant coefficient and one factor for each variable in the expression.
Step-by-step explanation:
For example, in the monomial 4x2y3, the factors are 4, x2, and y3. First, the coefficient is 4. The next factor, x2, is the x-factor, whose degree is 2.
A ball is thrown from an initial height of 7 feet with an initial upward velocity of 23 ft/s. The ball's height h (in feet) after 1 seconds is given by the following.
h = 7+23t-16t^2
Find all values of 1 for which the ball's height is 15 feet.
Answers
Answer:
Step-by-step explanation:
If we are looking for the time(s) that the ball is at a height of 15, we simply sub in a 15 for the height in the position equation and solve for t:
[tex]15=-16t^2+23t+7[/tex] and
[tex]0=-16t^2+23t-8[/tex]
Factor this however you factor a quadratic in class to get
t = .59 seconds and t = .85 seconds.
This means that .59 seconds after the ball was thrown into the air it was 15 feet off the ground. Then the ball reached its max height, gravity took over, and began pulling it back down to earth. The ball passes the height of 15 feet again on its way down after .85 seconds.
Evaluate z^2−3z+4, when z = −4
Answers
Answer:
32
Step-by-step explanation:
(-4)^2 -3(-4) +4=16+12+4
=32
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {32}}}}}}[/tex]
[tex]\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:\:EXPLANATION:}}}[/tex]
[tex] {z}^{2} - 3z + 4[/tex]
Plugging "[tex] -4[/tex]" for all values of "[tex]z[/tex]", we have
[tex] = ({ - 4})^{2} - 3( - 4) + 4[/tex]
[tex] = ( - 4 \times - 4) + 12 + 4[/tex]
[tex] = 16 + 12 + 4[/tex]
[tex] = 32[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Mystique35 }}{\red{❦}}}}}[/tex]
What is the solution to this equation?
6
O A. x = 18
O B. x= -2
O c. x= -18
O D. X= 21
Answers
O C. x = -18
Step-by-step explanation:
x/-3 = 6
x = denominator multiplied by quotient.
x = -3 x 6
x = -18
There are 40 children in a classroom and n of them do not wear spectacles. (4)/(5) of the boys and (2)/(3) of the girls wear spectacles. Express the number of boys who wear spectacles in terms of n.
Answers
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Answer:
b = 80 -6n . . . . boys who wear spectacles
Step-by-step explanation:
We know the ratio of boys who wear spectacles to those who don't is ...
(4/5) : (1 -4/5) = 4 : 1
If we let b represent the number of boys who wear spectacles, then the number who don't is b/4. Then total number of boys is then b +b/4 = 5b/4. The number of girls in the classroom is this number less than 40.
Let's define a few groups:
boys who wear spectacles: bboys who do not wear spectacles: b/4girls who wear spectacles: (2/3)(40 -5b/4)girls who do not wear spectacles (1/3)(40 -5b/4)Then the total of children who do not wear spectacles is ...
n = b/4 +(1/3)(40 -5b/4)
12n = 3b +(160 -5b) = 160 -2b . . . . multiply by 12
2b = 160 -12n . . . . . . . . . . . . . add 2b-12n
b = 80 -6n . . . . the desired relation, b = boys who wear spectacles
_____
Additional comment
The only values of n that make sense in this context are {8, 10, 12}, corresponding to {0, 15, 30} total girls and {40, 25, 10} total boys.
write your answer in simplest radical form
Answers
9514 1404 393
Answer:
f = 3 units
Step-by-step explanation:
The ratios of side lengths in this 30°-60°-90° triangle are ...
1 : √3 : 2
So, the ratio of interest is ...
1 : √3 = √3 : f
We can see that the numbers in the second ratio are √3 times the numbers in the first ratio, so
f = √3 × √3 = 3
f = 3 units
Suppose a jar contains 9 red marbles and 40 blue marbles. If 2 marbles are randomly chosen from the jar at
the same time, find the probability that both marbles are red. Round your answer to four decimal places.
Answers
Answer:
0.0306
Step-by-step explanation:
I don't know if there is any significance to both being drawn at the same time. I'm going to say there isn't.
The first draw gives
9/49
Their is no replacement. That's because both marbles are drawn together. The second draw is
8/48
P(both red) = 9/49 * 8 / 48 = 3/98 = 0.03061 which rounds to 0.0306
Hiiii can u please pls pls pls
Answers
Answer:
x | y
0 | 0
6 | 2
12 | 4
Step-by-step explanation:
Multiply each x value in the table by 1/3 to get 0, 2, and 4 for your y values.
Answer:
x y
0 0
6 2
12 4
Step-by-step explanation:
Is means equals
The equation is
y = 1/3 x
Let x = 0
y = 1/3 (0) = 0
Let x = 6
y = 1/3 (6) = 2
Let x = 12
y = 1/3 (12) = 4
I need some help! thank you!
Answers
Answer:
The 1st,Thrid, Fifth Option
Step-by-step explanation:
The first option is true. We can move the orginal square root function to get g(x).
The second option is false. Function g(x) which equals
[tex] \sqrt{x - 3} - 1[/tex]
Domain is all real numbers greater than or equal to 3.
The third option is true. Since minimum point we can get is 0 in a square root function. We have a vertical shift so our new minimum point is
[tex]0 - 1 = - 1[/tex]
We can take the sqr root of 0 so
So all real numbers that are greater than or equal to -1 is true.
The fourth option is false, we need to add 3 instead of subtract 3.
The fifth option is true, we can do that to get back to our original function
5(u-3)-3=-3(-6u+4)-3u
Answers
Answer:
u = -3/5
Step-by-step explanation:
5(u-3) - 3 = -3(-6u + 4) - 3u
(5u - 15) - 3 = (18u - 12) - 3u
5u - 18 = 15u - 12
-18 = 10u - 12
-6 = 10u
u = -6/10
u = -3/5
HELPP PLEASEEEEEEEEEEEEEEEEEEEEEE
The sum of 6 and 12 divided by 9.
Answers
18/9 = 2
The answer is 2
Hope this helps
−3 1/2 ÷ 1 1/4
khan academy
answer in simplified proper fraction
or
simplified improper fraction
Answers
Answer:
Step-by-step explanation:
Change the mixed numbers to improper fractions.
By the third day of a particular week, 2 accidents have already occurred in the intersection. What is the probability that there will be less than a total of 4 accidents during that week
Answers
Answer:
The right answer is "0.70".
Step-by-step explanation:
The given query seems to be incomplete. Please find below the attachment of the full query.
By using the Bayes' theorem, we get
⇒ [tex]P[(X<4)|(X \geq 2)] = \frac{P(2 \leq X < 4)}{P(X \geq 2)}[/tex]
By putting the values, we get
[tex]=\frac{[P(2)+P(3)]}{[1-P(0)-P(1)]}[/tex]
[tex]=\frac{(0.20+0.15)}{1-0.20-0.30}[/tex]
[tex]=\frac{0.35}{0.5}[/tex]
[tex]=0.70[/tex]
Which statement is true about the net and the solid it can form?
A. The length of side a will be 5 m.
B. The length of side b will be 2 m.
C. The length of side c will be 7 m.
D. The length of side c will be 2 m.
Answers
Step-by-step explanation:
Option B
The length of side will be 2m...
hope it helps
A classic counting problem is to determine the number of different ways that the letters of "Mississippi"can be arranged. Find that number.
Answers
Answer:
34, 650
Step-by-step explanation:
Given that,
The word = Mississippi
To find,
No. of different ways in which the letters of this word can be arranged = ?
Procedure:
Using the permutation rule as it is the case of repetition of identical items for finding the possibilities.
No. of letters in 'Mississippi' = 11
Letter 'i' appears = 4 times
Letter 's' appears = 4 times
Letter 'm' appears = 1 time
Letter 'p' appears = 2 times
So,
No. of possibilities = 11 ! ÷ (4 ! 4 ! 1 ! 2 !)
= (11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 *1)/(4 * 3 *2 * 1)(4 * 3 *2 * 1)(1)(2 * 1)
= 11 * 10 * 9 * 7 * 5
= 34,650
People's movements between places is called
Answers
Answer:
The three answers I can think of are migration, immigration, and emigration.
Step-by-step explanation:
Hope this helps!
If Sultan Akbar goes to the Grand Bazaar With 8000 Rupees and 20% is spent on a carpet, how much has the carpet cost him?
Si el sultan Akbar va al Gran Bazar Con 8000 Rupias y se gasta el 20 % en una alfombra, cuanto le ha costado la alfombra?
Answers
Answer:
1600 Rupees
Step-by-step explanation:
20 divided by 100 times 8000 will give you 1600 so the carpet costed him 1600
Lisa reads an equal number of pages of a book every week. The graph below shows the number of pages of the book left to read, y, after x weeks:
A graph titled Lisas Book Reading shows Number of Weeks on the x-axis and Number of Pages Left on the y-axis. The scale on the x-axis shows numbers from 0 to 6 at increments of 1, and the scale on the y-axis shows numbers from 0 to 350 at increments of 50. A straight line joins the ordered pairs 0, 250 and 1, 200 and 2, 150 and 3, 100 and 4, 50 and 5, 0.
Which equation best models the relationship between x and y?
y = −50x + 250
y = −5x + 50
y = −50x + 350
y = −5x + 250
Answers
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Answer:
(a) y = −50x + 250
Step-by-step explanation:
In case you don't realize that the graph starts at 250 and decreases by 50 for each increase of 1 in x, you can see if any of the equations match the given points. The only one that does is the first one:
y = -50x +250
Answer:
(a) y = −50x + 250
Step-by-step explanation:
Evaluate − x 2 −5 y 3 when x = 4 and y =−1
Answers
Answer:
-11
Step-by-step explanation:
I am going to assume that it is -x^2-5y^3.
-(4^2)-5(-1^3)
-16-5(-1)
-16+5
-11
Answer:
- 11
Step-by-step explanation:
If x = 4, y = -1
then,
- x^2 - 5y^3 = - (4)^2 - 5(-1)^3
= - 16 + 5
= - 11
which is the best stock you can invest now in 2021, or where I can learn to invest in stock market
Answers
Hope this helps! Please make me the brainliest, it’s not necessary but appreciated, I put a lot of effort and research into my answers. Have a good day, stay safe and stay healthy.
I need help with this it is very confusing.
Answers
Answer:
Part A: 90 + 6x = 108
Part B: 3
Step-by-step explanation:
Part A:
Variable x = number of movie tickets purchased
18 × 5 + 6x = 108
90 + 6x = 108
Part B:
Variable y = number of people
18y + 1(7) = 61
18y + 7 = 61
18y = 54
y = 3
There were 3 people in this group.
Which is heavier, 4- kilograms
or
4
4 kilograms?
Answers
Answer:
i think 4 4 kilograms if im wrong sorry
Step-by-step explanation:
identify the angles relationship
Answers
Adjacent
Step-by-step explanation:
Adjacent angles are two angles that have a common vertex and a common side but do not overlap
