Answer: d=18.2
Step-by-step explanation: d=2r=2·9.1=18.2
The gypsy moth is a serious threat to oak and aspen trees. A state agriculture department places traps throughout the state to detect the moths. When traps are checked periodically, the mean number of moths trapped is only 0.7, but some traps have several moths. The distribution of moth counts is discrete and strongly skewed, with standard deviation 0.8.
A) What are the mean and standard deviation of the average number of moths x in 60 traps?
B) Use the central limit theorem to find the probability (±0.01) that the average number of moths in 40 traps is greater than 0.4.
Answer:
a) The mean is 0.7 and the standard deviation is 0.1033.
b) 99.11% probability that the average number of moths in 40 traps is greater than 0.4.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
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].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
When traps are checked periodically, the mean number of moths trapped is only 0.7, but some traps have several moths. The distribution of moth counts is discrete and strongly skewed, with standard deviation 0.8.
This means that [tex]\mu = 0.7, \sigma = 0.8[/tex]
A) What are the mean and standard deviation of the average number of moths x in 60 traps?
60 traps means that [tex]n = 60[/tex]
By the Central Limit Theorem
Mean [tex]\mu = 0.7[/tex]
Standard deviation [tex]s = \frac{0.8}{\sqrt{60}} = 0.1033[/tex]
The mean is 0.7 and the standard deviation is 0.1033.
B) Use the central limit theorem to find the probability (±0.01) that the average number of moths in 40 traps is greater than 0.4.
40 traps means that [tex]n = 40[/tex]
Mean [tex]\mu = 0.7[/tex]
Standard deviation [tex]s = \frac{0.8}{\sqrt{40}} = 0.1265[/tex]
This probability is 1 subtracted by the pvalue of Z when X = 0.4. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.4 - 0.7}{0.1265}[/tex]
[tex]Z = -2.37[/tex]
[tex]Z = -2.37[/tex] has a pvalue of 0.0089
1 - 0.0089 = 0.9911
99.11% probability that the average number of moths in 40 traps is greater than 0.4.
5/8 plus 1/16 simplified
i’m having problems solving this too
Answer and Step-by-step explanation:
Half of them should be plain, so 46 plain bagels .
This is because the first set was split evenly, so that must mean this set should be split evenly as well.
Half of 92 is 46.
#teamtrees #PAW (Plant And Water)
What are the solutions of 3(x - 4)(2x - 3) = 0? Check all that apply.
-4
-3
- 를
c
3
4
Answer:
4 and 3/2
Step-by-step explanation:
[tex]x = 4 [/tex]
[tex]2x = 3 \\ x = \frac{3}{2} [/tex]
What’s the slop of the line in simplest form.
Answer:
y=1/2x +4
rise over run 1/2
y intercept is 4
Given that a = 2.4 cm, and b = 9.6 cm, work out x
Answer:
where am i supposed to find the x if you haven't given the equation for the sum
Step-by-step explanation:
The dimensions of a right rectangular prism are 3/2 ft, 1/2 ft, and 2ft. What is the volume of this prism ?
Answer:
v=1.5
Step-by-step explanation:
1.5*0.5*2=1.5
can i have brainliest
Volume of rectangular prism is 1.5 ft³
Given that;
Given prism is a right rectangular prism
Dimension are 3/2 ft, 1/2 ft, and 2ft
Find:
Volume of prism
Computation:
Volume of a rectangular prism = Length × Width × Height
Volume of rectangular prism = [3/2] × [1/2] × 2
Volume of rectangular prism = 6 / 4
Volume of rectangular prism = 1.5 ft³
Learn more;
https://brainly.com/question/12649592?referrer=searchResults
Which of the following shows the prime factorization of 200 using exponential notation?
Answer:
The prime factorization of 200 using exponential notation is [tex]2^{3}\times 5^{2}[/tex].
Step-by-step explanation:
First, we decompose the number given on statement by applying prime numbers in ascending order. We see that 200 is an even number, therefore, we infer that smallest prime number within is 2.
1) [tex]\frac{200}{2} = 100[/tex] (Even number)
2) [tex]\frac{100}{2} = 50[/tex] (Even number)
3) [tex]\frac{50}{2} = 25[/tex] (Even number)
4) [tex]\frac{25}{5} = 5[/tex] (Odd number, not a multiple of 3, but a multiple of 5 since last digit is 5)
5) [tex]\frac{5}{5} = 1[/tex] (Odd number, not a multiple of 3, but a multiple of 5 since last digit is 5)
Now, we construct the prime factorization using exponential notation:
[tex]200 = 2^{3}\times 5^{2}[/tex]
The prime factorization of 200 using exponential notation is [tex]2^{3}\times 5^{2}[/tex].
Answer:
2 * 3 * 5
Step-by-step explanation:
made a 100 on the text trust!!!!!
On a team, 7 girls and 2 boys scored a total of 46 points. The difference between the number of points scored by the 7 girls and the number of points scored by the
2 boys is 38. Each girl scored the same number of points and each boy scored the same number points. Find the number of points scored by each girl and each
boy
Answer:
Step-by-step explanation:
let the points scored by a girl=x
points scored by a boy=y
7x+2y=46
7x-2y=38
add
14x=84
x=84/14=6
7×6+2y=46
2y=46-42=4
y=4/2=2
girl scored =6 points
boy scored=2 points.
Bethany is a biologist who has been measuring and recording the rabbit population at a park over the last several years. She has noticed that a trigonometric function can model the population, which reaches a maximum population, m, each summer and a minimum population, n, each winter. If she uses to represent the rabbit population t years from the start of her study, what is the domain of function p?
Answer:
[0,∞)
Step-by-step explanation:
Answer:
[0,∞)
Step-by-step explanation:
Correct on Plato!
Find 22% of 48
Help please- i need this answer i’m stuck on it
Evaluate each expression if m= -4, n=1, p = 2, q=-6, r = 5, and t = -2.
|q-2mt|
Answer:
hi
Step-by-step explanation:
9xy + 5y +
what is the discounted price of a $15.50 with a 20% discount
Answer:
$12.40
Step-by-step explanation:
100% -20% discount = 80%
15.50 x 0.80 = 12.40
The perimeter of a rectangle is 62cm.if the length of the rectangle is 24cm,what is tge width of the rectangle
Answer:
b= 7
Step-by-step explanation:
here's your solution
=> perimeter of rectangle = 62 cm
=> length = 24 cm
=> let width be (b)
=> perimeter of rectangle = 2(l + b)
=> 2(l + b ) = 62
=> 2(24 + b) = 62
=> 48 +2b = 62
=> 2b = 62 - 48
=> 2b = 14
=> b = 14/2
=> b = 7
hope it helps
PLEASE HELP! I REALLY NEED HELP!!!
Answer:
on which one?
Write an equation of the line in slope-intercept from (answer fast pls )
Y=
Six hundred six and six hundredths in standard form.
Answer:
666
Step-by-step explanation:
all the numbers will be in number form instead of word form.
Given triangle ABC where
Please help me I really need it. Thanks!
Enrique collects miniature cars. He has one large case that holds 20 cars and 3 same-size, smaller cases to hold his cars.
Let n be the number of cars in each smaller case. Write an algebraic expression to represent how many total cars Enrique can fit in his cases.
Answer:
C = 3n + 20Step-by-step explanation:
There is one large case with 20 cars and 3 small cases with n cars in each.
Possible number of cars C is:
C = 3n + 20Write the decimal in simplest fractional form: -1.375
The consumption of asparagus results in the release of methanethiol and S-methyl thioesters metabolites in the urine. To some people, these metabolites have a very distinctive odor, but others cannot detect the odor ("asparagus anosmia"). How common is asparagus anosmia?
In a genetic study aiming to find the genetic markers supporting the phenotype, researchers contacted 6909 participants in a large scientific cohort and found that 4161 had asparagus anosmia. Assuming that the cohort is representative of the American adult population, obtain a 90% confidence interval for the true population of Americans with asparagus anosmia. Use technology, for instance, the 1-PropZInt function in the TI graphing calculator or the Statistics / Proportion / 1-sample function (Confidence Interval tab) on CrunchIt!.
Answer:
The 90% confidence interval for the true population of Americans with asparagus anosmia is (0.5926, 0.6120).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
Researchers contacted 6909 participants in a large scientific cohort and found that 4161 had asparagus anosmia.
This means that [tex]n = 6909, \pi = \frac{4161}{6909} = 0.6023[/tex]
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6023 - 1.645\sqrt{\frac{0.6023*0.3977}{6906}} = 0.5926[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6023 + 1.645\sqrt{\frac{0.6023*0.3977}{6906}} = 0.6120[/tex]
The 90% confidence interval for the true population of Americans with asparagus anosmia is (0.5926, 0.6120).
An automobile dealer can sell 12 cars per day at a price of $17,000. He estimates that for each $300 price reduction he can
sell two more cars per day. If each car costs him $14,000, and fixed costs are $1000, what price should he charge to
maximize his profit? [Hint: Let x = the number of $300 price reductions.]
How many cars will he sell at this price?
Answer:
$ 1100
Step-by-step explanation:
Let p(x) be the price he charges for a car after x price reductions.
Since car costs him $10,000, and fixed costs are $1000
p(x) = 13000-10000-1000-300x = 2000 - 300x
Let q(x) = 12 + 2x the quantity of cars sold after x price reductions.
and the profit he can make are given by:
Profit = R(x) = (12+2x)(13,000 - 10,000 - 1,000 - 300x) dollars.
As you can see, maximizing profit , we have to check where P'(x) = 0
And P''(x)<0.
So we get x = 3.
Replacing the value we get we get 2000 - 300 X 3 = 2000 - 900
= $ 1100
]
What is the approximate sector area.
(−1)^3⋅(−1)^2
simplify
What is the difference between the number of the students who prefer history to English?
Favorite Class
50
40
Number of Students
20
10
Math English Science History
Class
Pick one of these
55
35
45
10
Please help me
Will give you brainly
Answer:
They are 45 history students and 10 English students the difference is 35 students
35
HELLLLLPPPPPPPPP PLZZZZZZZZZZZZZZ
Answer:
D :)
Step-by-step explanation:
Because all of them are added by 12 constantly
Answer:
D
Step-by-step explanation:
because it represents 12 + x
1 + 12 = 13
2 + 12 = 14
etc
Find the volume of the irregular figure. 2 cm 3 cm 4 cm [?] cm3 5 cm 7 cm 3 cm 6 cm
No links for answers
Answer:
102cm³
Step-by-step explanation:
Imagine the shape as two rectangular prisms, a small one on top of a bigger one. Find their volumes individually, and then add them together:
Small rectangular prism
Volume=length*width*depth
=2*3*(7-5)
=6*2
=12cm³
Bigger rectangular prism
Volume=length*width*depth
=6*3*5
=6*15
=90cm³
12+90=102cm³
which expression is equivalent to the given expression (3m^2n)^3/mn^4
Answer:
Step-by-step explanation:
[tex]\frac{(3m^2n)^3}{mn^4}\\ \\ \frac{27m^6n^3}{mn^4}\\ \\ \frac{27m^5}{n}\\ \\ \text{ or if you want to use negative exponents}\\ \\ 27m^5n^{-1}[/tex]
In a small sporting good store there are 3 managers, 8
salesmen, and 5 cashiers. If a person is selected at random,
what is the probability that the person is a cashier or a
manager?
Answer:
1/2
Step-by-step explanation:
There are 16 people in total.
Cashiers and managers together total 8 people.
8/16 people are cashiers and managers, which equates to 1/2.
Write an equation to represent the hanger.
Explain how to reason to find the value of x.
Answer:
Step-by-step explanation: