Answer:
27x
Step-by-step explanation:
The packing machine is set to fill a cardboard box with a mean of 16.1 ounces of cereal. Suppose the amounts per box form a normal distribution with a standard deviation equal to 0.04 ounce.
(a) What is the probability of the boxes will end up with at least 1 pound of cereal?
(b) The seventy percent of the boxes will contain less than what number of ounces?
(c) Eighty percent of the boxes will contain more than what number of ounces?
(d) The middle 90% of the boxes will be between what two weights?
Answer:
a) 0.9938 = 99.38% probability that the boxes will end up with at least 1 pound of cereal
b) 16.121 ounces.
c) 16.0664 ounces.
d) Between 16.0342 and 16.1658 ounces.
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 16.1 ounces, standard deviation of 0.04 ounces. So
[tex]\mu = 16.1, \sigma = 0.04[/tex]
(a) What is the probability of the boxes will end up with at least 1 pound of cereal?
One pound is 16 ounces, so this is 1 subtracted by the pvalue of Z when X = 16. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{16 - 16.1}{0.04}[/tex]
[tex]Z = -2.5[/tex]
[tex]Z = -2.5[/tex] has a pvalue of 0.0062
1 - 0.0062 = 0.9938
0.9938 = 99.38% probability that the boxes will end up with at least 1 pound of cereal.
(b) The seventy percent of the boxes will contain less than what number of ounces?
Less than the 70th percentile, which is X when Z has a pvalue of 0.7. So X when Z = 0.525.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.525 = \frac{X - 16.1}{0.04}[/tex]
[tex]X - 16.1 = 0.525*0.04[/tex]
[tex]X = 16.121[/tex]
16.121 ounces.
(c) Eighty percent of the boxes will contain more than what number of ounces?
More than the 100 - 80 = 20th percentile, which is X when Z has a pvalue of 0.2. So X when Z = -0.84.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.84 = \frac{X - 16.1}{0.04}[/tex]
[tex]X - 16.1 = -0.84*0.04[/tex]
[tex]X = 16.0664[/tex]
16.0664 ounces.
(d) The middle 90% of the boxes will be between what two weights?
Between the 50 - (90/2) = 5th percentile and the 50 + (90/2) = 95th percentile.
5th percentile:
X when Z has a pvalue of 0.05, so X when Z = -1.645.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.645 = \frac{X - 16.1}{0.04}[/tex]
[tex]X - 16.1 = -1.645*0.04[/tex]
[tex]X = 16.0342[/tex]
95th percentile:
X when Z has a pvalue of 0.95, so X when Z = 1.645.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.645 = \frac{X - 16.1}{0.04}[/tex]
[tex]X - 16.1 = 1.645*0.04[/tex]
[tex]X = 16.1658[/tex]
Between 16.0342 and 16.1658 ounces.
It can be deduced that the probability of the boxes ending up with at least 1 pound of cereal will be 99.38%.
How to calculate the probabilityThe Z score based on the information will be:
Z = (16 - 16.1) / 0.04
Z = -2.5
Therefore, the p value is 0.0062. The probability will be:
= 1 - 0.0062
= 0.9938
The seventy percent of the boxes will contain less than 16 ounces. The ounces that will be contained in the eighty percent will be:
= -0.84 = (X - 16.1) / 0.04
X = 16
Lastly, the middle 90% of the boxes will be between 16.03 ounces 16.17 ounces.
Learn more about probability on:
https://brainly.com/question/25870256
GIVING OUT BRAINLIEST ANSWER HELP ME ASAP!!! pleaseeeee
Answer:
the answer is 29.7
Step-by-step explanation:
inverse tangent of (4/7)
Emma is training for a 10-kilometer race. She wants to beat her last 10-kilometer time, which was 1 hour 10 minutes Emma has already run for 55 minutes. Which inequality can be used to find how much longer she can run and still beat her previous time? (1 hr = 60 min)
A: 70>t-55
B: 70<t-55
Theres a line under the < For C
C: 70<t+55
D: 70>t+55
Answer:
c is the answer i dont know just here for the points
Step-by-step explanation:
i guess
For 11-14, fill in the blank with >, <, or =.
Answer:
first one is =
second one is ≥
third one is =
forth one is =
Can someone please help me?
Answer:
Question 1: The answer is "He could ask each person in his class who is the tallest person in the class."
Question 2: The mode is 56.
Step-by-step explanation:
Explanation 1: A statistical question is a question that can be answered by collecting data that varies. For example, “How old am I?" is not a statistical question, but “How old are the students in my school?” is a statistical question. Therefore, when we look at the options, the second option is the best.
Explanation 2: To find the mode we have to find which number is most frequent through out the set. When we look at the numbers, there are 3 numbers that have 56. Therefore, 56 is the mode.
What is the area of a Rectangle that 7 3/8 units long and 6 4/6 units wide?
Answer:
49 1/6
Step-by-step explanation:
Mark meh brainliest pls.
David and Patti each decomposed 138. David wrote 1 + 1/8 + 3/8. Patti wrote 4/8+2/8+5/8.
Who Is Correct?
No downloads
No Links
No files
No bitly.
Answer:
Both are wrong.
Step-by-step explanation:
We have that:
Both decomposed the fraction [tex]\frac{13}{8}[/tex] into a sum of fractions. Whoever's decomposition sum has a value of [tex]\frac{13}{8}[/tex] is correct.
David:
[tex]1 + \frac{1}{8} + \frac{3}{8} = \frac{8}{8} + \frac{1}{8} + \frac{3}{8} = \frac{8+1+3}{8} = \frac{12}{8}[/tex]
[tex]\frac{12}{8} \neq \frac{13}{8}[/tex], which means that David is wrong.
Patti
[tex]\frac{4}{8} + \frac{2}{8} + \frac{5}{8} = \frac{4+2+5}{8} = \frac{11}{8}[/tex]
[tex]\frac{11}{8} \neq \frac{13}{8}[/tex], which means that Patti is wrong.
So the answer is that both are wrong.
you are packing gifts for the annual holiday decorations the boxes you have been given measure 10 inches in length 6 in in within 12 inches in height the gifts this year smaller so you need smaller boxes you order new boxes with Dimensions that equal the dimensions of the large boxes times a scale factor of 1/2 what is the volume of each new box
Answer:
I dont know can u explaining more
Step-by-step explanation:
its not clear too much
Measurement of a circle
(Giving brainliest to correct answer)
Answer:
See below
Step-by-step explanation:
1. True
2. False
3. True
Point P lies on circle C, x^2+y^2=36. There are two unique tangents to circle D, x^2+y^2=18 that pass through point p. What is the measure of the angle between the two tangent lines?
Answer:
90°Step-by-step explanation:
Refer to attached
Red circle is C with radius 6 and green circle is D with radius √18.
PM and PN are tangents to circle D.
M and N are right angles as tangents are perpendicular to radius.
We need to find the measure of ∠MPN.
We'll work out this angle using trigonometry:
OM / OP = sin (∠MPO) sin (∠MPO) = √18/6 = √2/2m∠MPO = arcsin ( √2/2) = 45°∠NPO is same as ∠MPO, therefore:
m∠MPN = 45°*2 = 90°2(y-2)-2y=-8 simplify using substitution method
Answer:
Step-by-step explanation:
uhh i dont know much... can you explain it to me easier?
Answer:
responder dejar de engañar a idiota
Step-by-step explanation:
HElp And THAnkS ASAP
Answer:
B. M - J = 6
Step-by-step explanation:
Mike won 6 more games than Jeanie
so J + 6 = M
Subtract J from both sides of the equation
J - J + 6 = M - J
Simplify
6 = M - J
or
M - J = 6
Can the following lengths be
used to form a right triangle?
Explain.
Length 1: 15 units
Length 2: 20 units
Length 3: 35 units
Need help with functions
Step-by-step explanation:
in domian=-6,0
no in domian=2
Hey! I am stuck on this question anyone mind helping me? and tysm for the people who helped me! <3 have a nice day!
What is the value of u? (pls help and no links)
Answer:
I think 44 degrees
Step-by-step explanation:
73-29=44
Answer:
44
Step-by-step explanation:
The value of u, combined with the angle directly next to it (with the measurement of 29°), is a vertical angle to the opposite given angle (73°).
Note that, by the definition of vertical angles, angles directly next and opposite of each other have the same measurement. Set the equation:
u + 29 = 73
Isolate the variable, u. Note the equal sign, what you do to one side, you do to the other. Subtract 29 from both sides:
u + 29 (-29) = 73 (-29)
u = 73 - 29
u = 44
44° is your answer for u.
~
iif the pattern in the graph below continues, which of the following ordered pairs will lie on the line?
Select all that apply.
A. (14, 100)
B. (15, 100)
C. (16, 100)
D. (16, 120)
E. (18, 120)
Answer:
Step-by-step explanation:
B and E because the x axis always goes up by 3 and the y axis always goes up by 20
Answer:
Step-by-step explanation:
Find the distance between the two points.
(4,5)
(-4,1)
✓ [?]
Enter the number that
goes beneath the
radical symbol.
9514 1404 393
Answer:
80
Step-by-step explanation:
The distance formula tells you the distance between the points is ...
d = √((x2 -x1)² +(y2 -y1)²)
d = √((4 -(-4))² +(5 -1)²) = √(8² +4²) = √(64 +16)
d = √80
The number under the radical is 80.
use the distributive property to write equivpressions by filling in the blanks .
5(k+2) = (5+ __ ) + (5 ___ )
= __ + ___
Answer:
5(k+2) = (5 · k) + (5 · 2)
= 5k + 10
Answer:
5(k+2) = (5+ k+2 ) + (5 __k_ )
= _k_ + _2__ I may be wrong sorry
there's a 100 dollar stuck up 12 feet up a building and you buy a 15 foot ladder that can be safely leaned at a 60 degree angle, can you reach the bill?
Pls someone help me with this question pls
Answer:
c
Step-by-step explanation:
trust me i am did the test aredy
A die used in a certain board game has eight faces, of which 3 are red, 3 are yellow, and 2 are blue. Each face is equally likely to land faceup when the die is tossed. In the game, a player tosses the die until blue lands faceup, and the number of tosses before blue lands faceup is counted. For example, a player who tosses the sequence shown in the following table has tossed the die 3 times before blue lands faceup. What is the probability that a player will toss the die at least 2 times before blue lands faceup? A 0.1406 B 0.4219 C 0.4375 D 0.5625 E 0.5781
Answer: 0.5625
Step-by-step explanation:
Using the binomial distribution, it is found that the probability that a player will toss the die at least 2 times before blue lands face up is:
D 0.5625
For each toss, there are only two possible outcomes, either blue lands face up, or it does not. The probability of blue landing face up on a toss is independent of any other toss, which means that the binomial distribution is used to solve this question.
Binomial probability distribution
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes. n is the number of trials. p is the probability of a success on a single trial.In this problem:
2 out of the 8 faces are blue, hence [tex]p = \frac{2}{8} = 0.25[/tex]The probability that a player will toss the die at least 2 times before blue lands face up is P(X = 0) when n = 2, hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{2,0}.(0.25)^{0}.(0.75)^{2} = 0.5625[/tex]
Hence, option D is correct.
A similar problem is given at https://brainly.com/question/24863377
Find the volume.
pls help!!
Answer:
the answer to the problem is 48 km
Step-by-step explanation:
8*2*3
Answer: 48 sq km
Step-by-step explanation:
The length of the rectangular prism is 8 kilometers. The width is 3 kilometers. Lastly, the height is 2 kilometers. The formula for a rectangular prism is lwh, or length x width x height. 8 x 3 x 2 = 48 sq km.
Let z = 11 (cos(1) + i sin (1) and w=7(cos(1) + i sin (1)
What is zw?
A: 11/7(cos(pi/6) + i sin (pi/6)
B: 77(cos(pi/6)+ i sin (pi/6)
C:12(cos(pi/12) + i sin ( pi/12 )
D: 77 (cos(pi/12) + i sin (pi/12)
If a pyramid prism has a height of 12 ft and a square base with side = 10
ft. What is the surface are of the pyramid?
160 sq. ft
1,340 sq. ft
240 sq. ft
340 sq. ft
Find the area of the figure. HELP PLZ
Answer: 1075 sq. ft
Step-by-step explanation:
A = length times width
First split the shape into two rectangles
Area of rec 1 = 25 times 8 = 200
Area of rec 2 = 35 times 25 = 875
200+875 = 1075 sq. ft
17. Find the ratio of the perimeter to the area of the square shown.
x + 3
x + 3
Answer:
4x+12/x^2+9
Step-by-step explanation:
Perimeter
x+3+x+3+x+3+x+3
Area
(x+3)(x+3)
If you borrow $1500 for a year with a credit card that charges 26.8% annual interest, how much interest will you pay for the year?
Answer:
$402
Step-by-step explanation:
Interest = principal x rate x time
I = 1500 x .268
I = $402
Suppose that there are 27 sophomores and 14 juniors in a Physiology class. Two students are chosen at random to participate in a class demonstration. What is the
probability of choosing two students at random and the first is a junior and the second one is a sophomore? Round your answer to four decimal places, if necessary.
PLZ ANSWER NO FAKE LINKS OR SAYING I READY ISNT ALLOWED
Answer:
Answer 2 i think
i did it myself and that what got i might have done it wrong.