Answer:
if u carry the 7 by7 by 7 by 2 with devizon
Suppose that a random sample of 20 items is selected from the machine. If the machine produces 5% defectives, find the probability that the sample will contain at least three defectives, by using the following methods. (a) the normal approximation to the binomial (Round your answer to four decimal places.) (b) the exact binomial tables (Round your answer to three decimal places.)
Answer:
a) 0.0618 = 6.18% probability that the sample will contain at least three defectives.
b) 0.076 = 7.6% probability that the sample will contain at least three defectives
Step-by-step explanation:
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed 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.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
Sample of 20 items is selected from the machine.
This means that [tex]n = 20[/tex]
5% defectives
This means that [tex]p = 0.05[/tex]
(a) the normal approximation to the binomial
The mean is:
[tex]\mu = E(X) = np = 20*0.05 = 1[/tex]
The standard deviation is:
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{20*0.05*0.95} = 0.9747[/tex]
The probability is, using continuity correction, [tex]P(X \geq 3 - 2.5) = P(X \geq 2.5)[/tex] , which is 1 subtracted by the pvalue of Z when X = 2.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{2.5 - 1}{0.9747}[/tex]
[tex]Z = 1.54[/tex]
[tex]Z = 1.54[/tex] has a pvalue of 0.9382
1 - 0.9382 = 0.0618
0.0618 = 6.18% probability that the sample will contain at least three defectives.
(b) the exact binomial tables
This is:
[tex]P(X \geq 3) = 1 - P(X < 3)[/tex]
In which
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{20,0}.(0.05)^{0}.(0.95)^{20} = 0.358[/tex]
[tex]P(X = 1) = C_{20,1}.(0.05)^{1}.(0.95)^{19} = 0.377[/tex]
[tex]P(X = 2) = C_{20,2}.(0.05)^{2}.(0.95)^{18} = 0.189[/tex]
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.358 + 0.377 + 0.189 = 0.924[/tex]
[tex]P(X \geq 3) = 1 - P(X < 3) = 1 - 0.924 = 0.076[/tex]
0.076 = 7.6% probability that the sample will contain at least three defectives
Find the perimeter of the following shapes
3.6 cm
3 cm
7.2 cm
Step-by-step explanation:
Perimeter = 3.6 + 3 + 702
= 708.6 cm
28.
Car A and car B are 120 km apart. If they move towards each other, they will meet in 1 hour. If they
move in the same direction, car A will catch up with car B in 5 hours. Find the speed of car A and
the speed of car B. (Assume that the speeds of the cars are constant.)
i need help can you explain how to do it
Answer:
-7.
Step-by-step explanation:
(x²+t²x+t³+8)`=(x²)`+(t²x)`+(t³)`+(8)`=2x*x'+2t*x+t²*x'+3t²;
[tex]x'=\frac{2tx+3t^2}{t^2+2x};[/tex]
[tex]x'(-2;-4)=\frac{2*2*4+3*4}{4-8}=-7.[/tex]
HELP PLS MIGHT GIVE BRAINLIST BUT ONLY IF 2 PEOPLE ANSWER!
write the fraction 4/9 as an equivalent fraction with the given denominator 45
Answer:
answer is in the picture
A line that includes the point (-4, 9) has a slope of 1/2. What is its equation in point-slope
form?
Use the specified point in your equation. Write your answer using integers, proper fractions,
and improper fractions. Simplify all fractions.
Answer:
Hi Jewel, leave a comment if you want more explanation of the following:
Step-by-step explanation:
point-slope formula: y-y1 = m(x-x1)
slope-intercept formula: y = mx + b
using point-slope: y-9 = 1/2(x-(-4))
= y-9 = 1/2(x + 4)
= y -9 = 1/2x +2
we've almost made it to slope-intercept from , notice, but the problem says to leave it in point-slope form, so there you go :) and leave a comment if you need more explanations :)
Find the weight in pounds of a 140-kilogram person. Round to the nearest hundredth.
Answer:
308 pounds
Step-by-step explanation:
2.2 pounds /kg
2.2 x 140 = 308 pounds
HELP I WILL GIVE BRAINLEIST OR WHATEVER 50 POINTS
answer:
a. scarf costs today = $6
b. scarf costs 3 days from now = $3
step-by-step explanation:
1/2 off means you would multiply the amount by 1/2 then subtracta. original price of scarf: $12
12 X 1/2 = 6
12 - 6 = 6
— scarf costs today = $6
do the same thing but this time it is a different numberb. 12 X 3/4 = 9
12 - 9 = 3
— scarf costs 3 days from now = $3
Dawn bought 12 grams of chocolate. She ate half of the chocolate. How many grams of chocolate did she eat
A right prism has height 8 and triangular bases with sides of length 7, 8, and 9. What is the: Total surface area of the prism?
Answer:
the total surface area of the prism is 245.67
Step-by-step explanation:
Given;
height of the triangular prism, h = 8
length of the triangular bases, = 7, 8, and 9
The total surface area of the prism is calculated as;
T.S.A = ph + 2B
Where;
p is the perimeter of the base
B is area of the base
P = 7 + 8 + 9 = 24
Area of the base can be calculated using Hero's formula;
[tex]S = \frac{7+8+9}{2} = 12\\\\Base \ area (B) = \sqrt{12(12-7)(12-8)(12-9)} = 26.833[/tex]
T.S.A = (24 x 8) + 2 x 26.833
T.S.A = 192 + 53.666
T.S.A = 245.67
Therefore, the total surface area of the prism is 245.67
Two trains on opposite tracks leave the same station at the same
time. One train travels at an average speed of 80 kilometers per
hour and the other travels at an average speed of 70 kilometers
per hour. How long after they leave the station will they be 50
km apart?
Answer:
20 minutes( 0.3333 hours) after they leave the station will they be 50 km apart, if the Two trains on opposite tracks leave the same station at the same time.
Step-by-step explanation:
One train travels at an average speed of 80 km/hr and the other travels at an average speed of 70 km/hr.
2x - 3
L
M
x + 4
X =
?
Answer: 7
Step-by-step explanation:
2x - 3 = x + 4
2x - x - 3 = 4 Mius x from the both side
x - 3 = 4
x = 7 Add the 3 from both side
A cone in the diagram below has a radius (r) of 10mm and its height (h) is 24mm calculate the length of the slant height
Answer:
26mm
Step-by-step explanation:
by the Pythagorean theorem,
[tex]x^2=10^2+24^2\\x^2=676\\x=26[/tex]
PLZ HURRY, TIMED, WILL MARK BRAINLIEST********
K [Not drawn to scale] Which is true about the diagram? Select two options. MZIKH+MZIKL= 180° MZIKLU MZILK+mZKIL = 180° DmZJKH= MZJLK O MZIKLU MZILK= 90° OmZKIL= MZKLJ
Which would be a good estimate for the tax on $97.95 if the tax is 9.5%?
$12
$10.50
$10
$8.50
A piece of machinery depreciates 6000 the first year 5500 the second year and 5000 the third year. If the rate of depreciation is constant what is the amount of depreciation of the piece of the machinery in the sixth year?
Answer:
3500
hope this helps
Ran has 17 cameras to clean. He cleans 10 cameras.Then rah finds 8 more cameras to clean. How many cameras does ran has to clean now?
Answer:
total of 25 to clean.
did 10
has 15 left
Answer: 15
Step-by-step explanation:
Ran Needs to clean 17 cams... he already cleaned 10, so subtract 17-10... it would be 7
he finds 8 cams to clean... so we add 8+7... and it becomes 15...
brainliest appreciate
Question 3:
Hank is throwing a party. The party costs $20 per person. Answer the questions below to describe the relationship between the cost of the party and the number of friends attending.
The independent variable is .
The dependent variable is .
The equation that can be used to represent this relationship:
If 50 people attended, what would be Hank's cost?
(Only input numeric values, no commas, decimal points, or symbols.)
Answer:
$1000
Step-by-step explanation:
It would be $1000 in total of all the people attending the party. This is because, you need to multiply, 50 and 20! The answer will be 1000.
What is x(3x+2)?Please give a reasonable explaination and answer.
Answer:
3x squared + 2x as you multiply everything in the bracket by what's on the outside of the bracket so it would be 3x multiply by x which equals 3x squared and 2 multiply x which equals 2x
Answer:
3x^2+2x
Step-by-step explanation:
multiply each of the two terms by x using the distributive property
Patrick randomly selects a marble from a bag , records the color and then returns the marble to the bag . After 40 trials , he has recorded 14 red marbles 12 blue marbles yellow marbles and 4 green marbles Which of the following experimental probabilities is correct based on his record ?
Answer: A
Step-by-step explanation:
(Write a sentence equation ) There are 3 lambs .Each lamb has 4 legs. How many legs are there on 3 Lambs?
Answer:
Well its basically 3 x 4 = 12, so for every lamb add four legs until you get to three
Step-by-step explanation:
6 or -11 ( < or >) which describes the relationship between the numbers?
Answer:
6 ( > ) -11
Step-by-step explanation:
6 is bigger than -11
The width of a rectangle is represented by 5 - 2y.
The length is twice as long as the width What is the
perimeter of the rectangle? Select all correct expressions
A45-27
3 65 - 27
C20 -
D30 - 12
Answer:
Perimeter of rectangle = 30 - 12y
Step-by-step explanation:
Given:
Width of rectangle = 5 - 2y
Length of rectangle = 2(width) = 2[5 - 2y] = 10 - 4y
Find:
Perimeter of rectangle
Computation:
Perimeter of rectangle = 2[l + b]
Perimeter of rectangle = 2 [10 - 4y + 5 - 2y]
Perimeter of rectangle = 2[15 - 6y]
Perimeter of rectangle = 30 - 12y
The measure of an angle is 149.5°. What is the measure of its supplementary angle?
Answer:
30.5°
Step-by-step explanation:
Supplementary angles add up to 180°. You know one angle is 149.5°, so you can find the other angle.
Measure of its supplementary angle = 180° - 149.5°
= 30.5°
Help please I need this
Answer:
12
13
89
Step-by-step explanation:
ez pz
i need help ////////
Answer:
[tex]1\frac{1}{2}[/tex] miles = 7920 feet
2[tex]\frac{1}{2}[/tex] miles = 13200 feet
3[tex]\frac{1}{2}[/tex] miles = 18480 feet
4[tex]\frac{1}{2}[/tex] miles = 23760 feet
5[tex]\frac{1}{2}[/tex] miles = 29040 feet
6[tex]\frac{1}{2}[/tex] miles = 34320 feet
Explanation:
1 mile = 5280 feet
[tex]\frac{1}{2}[/tex] miles = 2640 feet
to convert miles into feet, multiply the whole numbers by 5280 and add 2640 to find your overall feet
2[tex]\frac{1}{2}[/tex] : 2 x 5280 + 2640 = 13200 ft
3[tex]\frac{1}{2}[/tex] : 3 x 5280 + 2640 = 18480 ft
4[tex]\frac{1}{2}[/tex] : 4 x 5280 + 2640 = 23760 ft
5[tex]\frac{1}{2}[/tex] : 5 x 5280 + 2640 = 29040 ft
6[tex]\frac{1}{2}[/tex] : 6 x 5280 + 2640 = 34320 ft
a sector has a radius of 4 and a central angle of 40 degrees. Find the arc length and area of sector
Answer:
Step-by-step explanation:
θ = 2π/9 radians
arc length = rθ = 8π/9 units
area of sector = πr²/9 = 16π/9 square units
Simplify: 17b + 82c + 90 + e - 18 - 10c - b
which of the following phrases describes the expression 2 - 2x
Answer:c
Step-by-step explanation:cccccc