Answer:
a) 1 = 100% probability that at least one sample will contain one or more bacterial colonies.
b) 1 sample should be selected in order to have a probability of approximately 0.95 of seeing at least one bacterial colony
Step-by-step explanation:
To solve this question, we need to understand the poisson and the binomial distributions.
Poisson distribution:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
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.
Probability of a single sample having at least one bacterial colonies.
Poisson distribution with a mean of 3 per cubic centimeter (cm3), which means that [tex]\mu = 3[/tex]
This is:
[tex]P(X \geq 3) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-3}*3^{0}}{(0)!} = 0.0495[/tex]
[tex]P(X \geq 3) = 1 - P(X = 0) = 1 - 0.0495 = 0.9505[/tex]
(a) If eight 1 cm3 samples are independently selected from this water, find the probability that at least one sample will contain one or more bacterial colonies.
Multiples samples means that the binomial distribution is used.
0.9505 probability of a sample having at least one colony, which means that [tex]p = 0.9505[/tex]
8 samples means that [tex]n = 8[/tex]
The desired probability is:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{8,0}.(0.9505)^{0}.(0.0495)^{8} \approx 0[/tex]
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0 = 1[/tex]
1 = 100% probability that at least one sample will contain one or more bacterial colonies.
(b) How many 1 cm3 samples should be selected in order to have a probability of approximately 0.95 of seeing at least one bacterial colony
We have to find [tex]P(X \geq 1)[/tex] for samples of 1,2,3,..., until this probability is 0.95. So
n = 1
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{1,0}.(0.9505)^{0}.(0.0495)^{1} = 0.0495[/tex]
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0495 = 0.9505[/tex]
0.9505 > 0.95
1 sample should be selected in order to have a probability of approximately 0.95 of seeing at least one bacterial colony
math come help plese
Answer:
74
Step-by-step explanation:
Can someone help please, please no dirty links you will be reported.
Answer:
3.25
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What rational number is equivalent to .36 repeating
Answer:
4/11
Step-by-step explanation:
i think,,,,try it and maybe its right
A cookie jar contains 3 vanilla, 2 chocolate chip, and 7 gingersnap cookies. If one cookie is taken at random from the jar, what is the probability that it will be a vanilla cookie?
Answer:
3/12= 1/4
Step-by-step explanation: because you would add the all up for 12 and you have a 3 vanilla's so 3/12= 1/4
3x+12 greatest common factors
Answer:
The common factors for 3,12 are −3,−1,1,3 - 3 , - 1 , 1 , 3 .
Step-by-step explanation:
A company makes 150 bags.
23 of the bags have buttons but no zips.
35 of the bags have zips but no buttons.
49 of the bags have neither zips nor buttons.
How many bags have zips on them?
What's greater? 18% or 11/55?
Answer:
11/55
Step-by-step explanation:
11/55 = 20%
18% = 18%
Answer:
11/55 is greater
Step-by-step explanation:
18% is less because divided by 100 it will be 0.18 and if you multiply 11/55 the answer is 0.20
A water balloon was launched into the top of the hill 38 feet above the ground
Answer: -71.104 ft/sec
Step-by-step explanation:So you need to know how fast the balloon is moving when it hits this person's head. velocity is based on time. So you need the time that it hits this person's head. You can get time from the position equation. Because the balloon hits this person's head 6 feet from the ground, you know that the final position is at 6 so you plug that into the position equation and solve for t. You look and see what the appropriate t value is and plug it into the velocity equation and see what the answer is.
6=-16t^2+40t+60
0=-16t^2+40t+54
plug in those values into the quadratic formula or your calculator and you get:
t = -.972
or
t = 3.472
since you can't have negative time, the other answer must be it.
So you then plug it in and solve.
v(3.472) = -32(3.472) + 40
which is approximately -71.104 ft/sec
or if they just want speed, 71.104 ft/sec. (remember, speed is velocity without direction)
18, 12, 8, ...
Find the 10th term.
Answer:
-24
Step-by-step explanation:
18, 12, 8, 4, 0, -4, -8, -12, -18, -24
You are going down by 4 so by the time you get to the 10th term it will be a negative.
Si a y b son los catetos de un triángulo y c su hipotenusa determina el lado que falta a= 16,b=34*
Answer:
the aswer is b
Step-by-step explanation:
i
PLEASE HELP!!!
I’ve been working on this equation for 2 days now and can’t get the right answer I think this is the right way to do it but I’m not sure
Solve for Y in the equation (5y-29) + (3y+19) = 180
Answer:
A - they are vertical angles so they are equal to each other
b - dont really know this one
c - y=24 and 7 and 8 = 89
Step-by-step explanation:
You messed up because the angles given are not supplementary the angles given that are next to 7 and 8 are vertical then we can setup an equation which would be 5y-29=3y+19 and solve for y
step 1 add 29 to each side
5y=3y+48
step 2 subtract each side by 3y
2y=48
step 3 divide each side by 2
y=24
then we plug in 24 to one of the expressions
5(24)=120
120-19=101
but we are not done yet because it is asking for the value of angle 7 and 8
because angle 7 is supplementary to both all we have to do is subtract 101 from 180
180-101=89 so 7 and 8 =89
hope this helps :D
Find the missing side of this right triangle. [Pythagorean Theorem]
Answer: 12 x 7 = 72
Step-by-step explanation:
Answer:
Square root of 193
Step-by-step explanation:
7^2+12^2=x^2
Switch sides: x^2=7^2+12^2
After everything is squared: x^2=49+144
x^2=193 OR x=\sqrt{193}
Need help I will offer brainalist + 10 points for correct answer (:
Plz help if correct ill give brailiest
Answer:
At most 5
At least 0
Step-by-step explanation:
22 - 17 = 5
You can't have no more than 5, and you can have none join at all.
Answer:
At the most, it will be 5
At least it will be 0
You can't have anymore than 5, and you can have none join at all.
Step-by-step explanation:
22 - 17 = 5
You can't have anymore than 5, and you can have none meet at all.
Find the area of the rhombus. Each indicated distance is half the length of it’s respective diagonal.
(image included)
Answer:
384 ft²
Step-by-step explanation:
12x16x2=384
A raffle is going to be held in which the winner will get $200. If 1000 tickets are to be sold, what is the fair
price for a ticket?
Answer:
$5
Step-by-step explanation:
1000/200=5
Answer:
20 cents.
Step-by-step explanation:
A fair price would be 200/1000 = 1/5 of a dollar which is 20 cents. But this does not allow for the people putting on the raffle to make any money for doing it. It would be better if the raffle went for a dollar. Most people would think that is fair and would not begrudge a dollar.
I need help with this question please, if anyone would be kind enough to give me the correct answer, in return I would gladly rate a 5 star and give brainliest (:
at which approximate rate in feet per minute did the plane climb to the cruising altitude of 35,000 feet
An airplane is flying diagonally across the state of Colorado. This state and its
dimensions are represented by the rectangle on the map shown.
280 mi
385 mi
Based on the measurements shown in the map, which measurement is closest to the
distance in miles the airplane will fly along the diagonal?
A
665.0 mi
B
25.8 mi
с
36.4 mi
D
476.1 mi
Please help
See the picture
Answer:
6
Step-by-step explanation:
Gud luck
I will give extra points please help
Answer:
9
Step-by-step explanation:
45/5 = 9
What is the solution to the system of equations?
y = 2/3x + 3
x=-2.
Write 11/8 as a mixed fraction
Answer:
1 3/8
Step-by-step explanation:
Since 11 is over 8 that means you already have a whole number so you just add the 3 and you get 1 3/8
To check just in case you just multiply the whole number and denominator and then add the numerator.
In a survey of 526 visitors to the craft center, 378 want the craft center to be open later in the evenings. What is the interval that is likely to contain the true population proportion?
37% to 69%
16% to 17%
20% to 38%
0% to 53%
Answer:
37% to 69%
Step-by-step explanation:
23, 75, 79, 99, 105, 110, 110, 142, 149, 168, 168, 170, 183, 195, 202
Find the IQR, show your work.
HELP!
Answer:
the IQR is 71
Step-by-step explanation:
the Xl is 99 and the Xu is 170. Xu-Xl=71
Simplify -3 p3 + 5 p + (-2 p2 ) + (-4) - 12 p + 5 - (-8 p3 ). Select the answer in descending powers of p . 1 - 7 p - 2 p2 + 5 p3 1 + 7 p + 2 p2 - 5 p3 5 p3 - 2 p2 - 7 p + 1 -5 p3 + 2 p2 + 7 p + 1
Step-by-step explanation:
Let's simplify step-by-step.
−3p3+5p−2p2−4−12p+5−−8p3
=−3p3+5p+−2p2+−4+−12p+5+8p3
Combine Like Terms:
=−3p3+5p+−2p2+−4+−12p+5+8p3
=(−3p3+8p3)+(−2p2)+(5p+−12p)+(−4+5)
=5p3+−2p2+−7p+1
Answer:
=5p3−2p2−7p+1
The formula for the circumference, C, of a circle with given radius, r, is C = 2πr. meters? what is the circumference of a circle with a radius of 3 1/2 meters? (use 22 as an estimate for it.)
A. 7 meters
B. 11 meters
C. 22 meters
D. 44 meters
Answer:
22
actual answer was 21.99
Alexis is going to Vegas for the weekend! She decides to try her hand at a new game that Casino QuickCash is promoting. For this game, you pay $6 to play. A dealer shuffles and then randomly draws a card from a standard deck of 52 cards. If the card drawn is a diamond, Alexis wins nothing. If the card drawn is an even-numbered card (2,4,6,8, or 10) from the remaining three decks, Alexis wins $8. Otherwise, Alexis wins $12. a) Alexis's expected winnings per game is (rounded to the nearest cent):
Answer:
$10.46
Step-by-step explanation:
Amount that can be won by Alexis ( xi ) = $0, $8 , $12
probability ( pi )
P( $0 ) = 13 / 52 = 1 / 4
P( $8 ) = 15 / 39 ( given that she wins this when an even number is drawn from three remaining decks )
P ( $12 ) = 1 - 15/39 = 24 / 39
a) Alexis expected winnings per game
= ∑ xi * pi = ( 0 * 1/4 ) + ( 8 * 15/39 ) + ( 12 * 24 / 39 )
= $0 + ( 120 / 39 ) + ( 288 / 39 ) = $10.46
ТDaP is a booster shot that prevents Diphtheria, Tetanus, and Pertussis in adults and adolescents. It should be administered every 8 years in order for it to remain effective. A random sample of 500 people living in a town that experienced a pertussis outbreak this year were divided into two groups. Group 1 was made up of 132 individuals who had not had the TDaP booster in the past 8 years, and Group 2 consisted of 368 individuals who had. In Group 1, 15 individuals caught pertussis during the outbreak, and in Group 2, 11 individuals caught pertussis. Is there evidence to suggest that the proportion of individuals who caught pertussis and were not up to date on their booster shot is higher than those that were? Test at the 0.05 level of significance.
Enter the test statistic - round to 4 decimal places.
Enter the P-Value - round to 4 decimal places.
Is there evidence to suggest the proportion of those who caught pertussis is higher for those who were not up to date on their booster?
Answer: 76.8356 and 12.5372
Step-by-step explanation:
This Question: 1 pt
17 of 29
Emma has $160 cash to spend at a music store. How much can she spend on items if there is a 7% sales tax?
Emma can spend on items.
(Round to the nearest cent as needed.)
Answer:
i would say $148.80
Step-by-step explanation:
tax would amount to 11.20 so when you subyract that from the total then the rest is what she can spend.