Answer:
a) 0.1587 = 15.87% probability that a battery will last more than 20 hours.
b) 15.44 hours.
c) Approximately the 16th percentile.
d) 0.1974 = 19.74% probability that the lifetime of a battery is between 17.5 and 18.5.
e) 0.5704 = 57.04% probability that the mean lifetime is between 17.5 and 18.5
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 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].
In this question, we have that:
[tex]\mu = 18, \sigma = 2[/tex]
(a) What is the probability that a battery will last more than 20 hours?
This is 1 subtracted by the pvalue of Z when X = 20. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{20 - 18}{2}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a pvalue of 0.8413
1 - 0.8413 = 0.1587
0.1587 = 15.87% probability that a battery will last more than 20 hours.
(b) Find the 10th percentile of the lifetimes.
This is X when Z has a pvalue of 0.1. So X when Z = -1.28
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.28 = \frac{X - 18}{2}[/tex]
[tex]X - 18 = -1.28*2[/tex]
[tex]X = 15.44[/tex]
So 15.44 hours.
(c) A particular battery lasts 16 hours. What percentile is its lifetime on?
We have to find the pvalue of Z when X = 16. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{16 - 18}{2}[/tex]
[tex]Z = -1[/tex]
[tex]Z = -1[/tex] has a pvalue of 0.1587
Approximately the 16th percentile.
(d) What is the probability that the lifetime of a battery is between 17.5 and 18.5?
This is the pvalue of Z when X = 18.5 subtracted by the pvalue of Z when X = 17.5. So
X = 18.5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{18.5 - 18}{2}[/tex]
[tex]Z = 0.25[/tex]
[tex]Z = 0.25[/tex] has a pvalue of 0.5987
X = 17.5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{17.5 - 18}{2}[/tex]
[tex]Z = -0.25[/tex]
[tex]Z = -0.25[/tex] has a pvalue of 0.4013
0.5987 - 0.4013 = 0.1974
0.1974 = 19.74% probability that the lifetime of a battery is between 17.5 and 18.5.
(e) Ten batteries are chosen at random, what is the probability that the mean lifetime is between 17.5 and 18.5?
Sample of 10 means that, by the Central Limit Theorem, [tex]n = 10, s = \frac{2}{\sqrt{10}} = 0.6325[/tex]
X = 18.5
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{18.5 - 18}{0.6325}[/tex]
[tex]Z = 0.79[/tex]
[tex]Z = 0.79[/tex] has a pvalue of 0.7852
X = 17.5
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{17.5 - 18}{0.6325}[/tex]
[tex]Z = -0.79[/tex]
[tex]Z = -0.79[/tex] has a pvalue of 0.2148
0.7852 - 0.2148 = 0.5704
0.5704 = 57.04% probability that the mean lifetime is between 17.5 and 18.5
Help meeeeeeeeeeeeeeeeeeeeee
Answer:
The equation model for the transformed graph f(x) = -5×+ 3 -6.
HELP PLSSSSS I BEG YOUUUUUUUUUUUUUUUUU
Answer:
just shade in the same thing
just shade in the same thing
f(x)=3x(x^2+4x-5) evaluate f(-2)
Answer:
f(-2) = 54
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
f(x) = 3x(x² + 4x - 5)
f(-2) is x = -2
Step 2: Evaluate
Substitute in x [Function]: f(-2) = 3(-2)[(-2)² + 4(-2) - 5][Brackets] Evaluate exponents: f(-2) = 3(-2)[4 + 4(-2) - 5][Brackets] Multiply: f(-2) = 3(-2)[4 - 8 - 5][Brackets] Subtract: f(-2) = 3(-2)[-4 - 5][Brackets] Subtract: f(-2) = 3(-2)(-9)Multiply: f(-2) = -6(-9)Multiply: f(-2) = 54A rectangular prism has a length of 312 inches, a width of 312 inches, and a height of 7 inches. Danny has a storage container for the prism that has a volume of 90 cubic inches.
What is the difference in volume between the prism and the storage container?
Answer:
The answer is 429 meters
Step-by-step explanation:
I took the test and got it correct
A kite is shown below with given dimensions in inches. What is the area in square units
Answer:
320
80
Step-by-step explanation:
whats 1+0+9+5+5+3+9+3+112-123+7-7x0
Step-by-step explanation:
First, multiply -7 by 0.
-7×0=0
Now, do the adding and subtracting.
1+0=1
1+9=10
10+5=15
15+5=20
20+3=23
23+9=32
32+3=35
35+112=147
147-123=24
24+7=31
31+0=31
The answer is: 31
In a certain city, the population mean commute time to work was reported as 30 minutes. The director of human resources for a certain company in the city claimed the mean commute time for the
company's employees was greater than 30 minutes. The director surveyed 35 randomly selected employees and found that their mean commute time was 31.4 minutes. With all conditions for
inference met, a hypothesis test conducted at the significance level a = 0.05 resulted in a p-value of 0.381
Which of the following is an appropriate conclusion?
Answer:
Answer.The director does not have convincing statistical evidence to conclude that the population mean commute time is greater than 30 minutes.
Because the p value is very high and higher than level of significance ,so we fail to reject null hypothesis.
PLEASE HELP ME BEST ANSWER GETS BRAINLIEST NO SCAMS PLEASE!
This is an example of a random sample: Surveying people in the library about whether they like to read books.
True
False
Answer:
False
Step-by-step explanation:
People reading in a library are most likely going to like to read books
Answer:
false i thin if not sorry
Step-by-step explanation:
YEE YEE
Find the volume of each prism 6B+4 3/4H+ 6L in. WHOEVER ANSWERS FIRST GETS 30 PTS!!!!
Answer:
Okay, im sorry i have no idea how to work dis
in a class the ratio of boys to girls is 3/2. if there are 12 boys in the class, how many girls are there?
Answer:
8
Step-by-step explanation:
3 times 4 is 12 and 2 times 4 is 8
Which of the following shapes have an area of 48 square feet? Select all that apply.
A scalene triangle with a base of 8 feet and a height of 6 feet.
A right triangle with a base of 9 feet and a height of 10 2/3 feet.
A rectangle with a base of 19.2 feet and a height of 2.5 feet.
A parallelogram with a base of 16 feet and a height of 3 feet.
Jake needs a new camera for school. He has already saved $110 and he earns $9 per hour in a photography internship.
If the equation s = 9h + 110 represents that relationship, how many hours will he need to work (h) in order to save (s) $425 to purchase
his camera?
Help
DO THIS FOR BRAINLIEST PLEASE
Joey wants to find out what sport 7th grade girls like the most. He asks "Is basketball your favorite sport?"
This question is biased.
True OR False
Answer:
True
Step-by-step explanation:
I hope I'm right
Answer:
False
Step-by-step explanation:
No 7th grade girl likes basketball the most unless they're going through their tomboy phase of life.
Clare bought an expensive
for £38 000 and sold it 3 years later
for £25 000. Find the percentage loss
that she made on the sale. (1 dp)
The prism shown has a volume of 35 cm^3
Work out h, the height of the triangular cross section.
Length =7 cm
Base=4 cm
Answer:
[tex]Height = 2.5[/tex]
Step-by-step explanation:
Given
[tex]Volume = 35[/tex]
[tex]Length =7[/tex]
[tex]Base=4 cm[/tex]
Required
Determine the height
The volume is calculated as:
[tex]Volume = Height * Base\ Area[/tex]
Since, it has a triangular cross-section, the expression becomes:
[tex]Volume = Height * \frac{1}{2} * Base * Length[/tex]
So, we have:
[tex]35 = Height * \frac{1}{2} * 4 * 7[/tex]
[tex]35 = Height * 14[/tex]
[tex]Height = 35/14[/tex]
[tex]Height = 2.5[/tex]
Simplify 8+5h-2+h-10+3h
Answer:
-4+7h
Step-by-step explanation:
Answer:
9h-4
Step-by-step explanation:
8+5h-2+h-10+3h
-4+5h+h+3h
Can somebody plz tell me which one is congruent or supplementary
Can someone please help me?
Answer:
#25 is left, #27 is between, #28 is below, and #26 is first i think.
Step-by-step explanation:
Answer: #25 is left, #27 is between, #28 is below, and #26 is first i think.
Step-by-step explanation:
Use a double number line to answer Problem 1-5.
Tanner collected 360 cans and bottle while fundraising for his baseball team. This eas 40% of what Reggie collected. How many cans and bottles dif Reggie collect?
Answer:
900 cans and bottles.
Hope that helps!
Step-by-step explanation:
360 / 4 = 90
90 x 100 = 900
Hope that helps!
Please Help. Will give Brainliest.
Answer:
translation.........
Simplify the following:
2x^3-3x^2+4x+5 / x+2
Show steps! Please help for college prep math
answer:
2x^3-3x^2+9x+2
step-by-step explanation:
i added 4x and 5x to get 9x
good luck :)
hopefully, this helps
have a great day !!
The length of Andy's bed is 123 what is the length in feet
Answer:
4.068 feet
Step-by-step explanation:
carolette is making necklace's in blue and orange her ratio of blue beads to orange beads are 3 to 2 how many beads will carolette need for a necklace of 60 beads
Answer:
Carlotta needs 24 orange beads for her necklace.
Step-by-step explanation:
For each necklace, the ratio of blue beads to orange beads is 3 to 2. or 3:2
Total beads given to make a necklace is = 60
Let the number of orange beads be = x
The ratio is 2 orange beads out of 5 total beads
So, we can represent the ratio as:
x=24
Hence, Carlotta needs 24 orange beads for her necklace.
Blue beads needed =
We can also check the ratio for blue beads to orange beads:
Divide by 4, we get
Divide by 3, we get
...... (the given ratio)
Therefore, Carlotta needs 24 orange beads for her necklace
Which choice shows 1/4 of 8
Answer:
there is no picture so I dont know what i have to do..
simplificar y sumar
12 + 7 + 10 =
---- ---- ---
Answer:
12 + 7 = 19
19 + 10 = 29
answear = 29
what is the slope of (4,7) (9,7)?! please help i tried omni and it didn't give me an answer
Answer:
0
Step-by-step explanation:
Question 5
What is the equation of the line?
Answer:
y = -3× + 1
Step-by-step explanation:
rise / run = 3 / -1 = -3
y intercept = 1
therefore y = -3× + 1
In the first 15 seconds of the rollercoaster, passengers are carried up a 90-meter hill, plunged down 62 meters, and quickly taken back up a 38-meter rise. How much higher or lower from the start of the ride are they after these 15 seconds?
Answer:
90-62=28
28+38=66
90-66=24
in 15 seconds they are 24 meters lower
If a translation maps zl onto ZK, which of the following statements is true? G HS 1 K НІ is twice the measure of 2JK: GH is twice the measure of 2GJ: Triangles AGHI and AGJK are not similar. OCH = J
9514 1404 393
Answer:
(d) ∠H ≅ ∠J
Step-by-step explanation:
We already know that ∠G is congruent to itself. If we show (by translation or other means) that ∠I ≅ ∠K, then we know that ΔGHI ~ ΔGJK. The third angle in each triangle will be congruent, too.
∠H ≅ ∠J
_____
The problem is concerned with angles, so the first two answer choices are irrelevant. If two angles are shown congruent, the triangles are congruent by AA similarity, so the third answer choice is incorrect.
Answer: D
Step-by-step explanation:
2) The difference of two numbers is 13. Their sum is 85. Find the numbers.
What’s the answer
Answer:
49 and 36
Step-by-step explanation:
49 - 36 = 13
49 + 36 = 85
Answer:solving we get y=6 x+y=85
x-y=13
add the equations
2x=98
x=98/2
x=49
85-49=36
the numbers are 49 and 36
Hope this helps have a awesome night/day❤️✨
Step-by-step explanation: