Answer:
a) 59.10% probability that 12 or fewer fish were caught.
b) 99.74% probability that 5 or more fish were caught.
c) 58.84% probability that between 5 and 12 fish were caught.
Step-by-step explanation:
I am going to use the normal approximation to the binomial to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
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 samples 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].
In this problem, we have that:
[tex]n = 29, p = 0.41[/tex]
So
[tex]\mu = E(X) = np = 29*0.41 = 11.89[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = 2.6486[/tex]
Find the following probabilities.
a) 12 or fewer fish were caught.
Using continuity correction, this is [tex]P(X \leq 12 + 0.5) = P(X \leq 12.5)[/tex], which is the pvalue of Z when X = 12.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{12.5 - 11.89}{2.6486}[/tex]
[tex]Z = 0.23[/tex]
[tex]Z = 0.23[/tex] has a pvalue of 0.5910
59.10% probability that 12 or fewer fish were caught.
b) 5 or more fish were caught.
Using continuity correction, this is [tex]P(X \geq 5 - 0.5) = P(X \geq 4.5)[/tex], which is 1 subtracted by the pvalue of Z when X = 4.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{4.5 - 11.89}{2.6486}[/tex]
[tex]Z = -2.79[/tex]
[tex]Z = -2.79[/tex] has a pvalue of 0.0026
1 - 0.0026 = 0.9974
99.74% probability that 5 or more fish were caught.
c) between 5 and 12 fish were caught.
Using continuity correction, this is [tex]P(5 - 0.5 \leq X \leq 12 + 0.5) = P(4.5 \leq X \leq 12.5)[/tex], which is the pvalue of Z when X = 12.5 subtracted by the pvalue of Z when X = 4.5. So.
From a), when X = 12.5, Z has a pvalue of 0.5910
From b), when X = 4.5, Z has a pvalue of 0.0026.
So
0.5910 - 0.0026 = 0.5884
58.84% probability that between 5 and 12 fish were caught.
A study reports that college students work, on average, between 4.63 and 12.63 hours a week, with confidence coefficient .95. Which of the following statements are correct?MARK ALL THAT ARE TRUE.There are four correct answers. You must mark them all to get credit.A. The interval was produced by a technique that captures mu 95% of the time. B. 95% of all college students work between 4.63 and 12.63 hours a week. C. 95% of all samples will have x-bar between 4.63 and 12.63. D. The probability that mu is between 4.63 and 12.63 is .95. E. 95% of samples will produce intervals that contain mu. F. The probability that mu is included in a 95% CI is 0.95. G. We are 95% confident that the population mean time that college students work is between 4.63 and 12.63 hours a week.
Answer:
Step-by-step explanation:
Confidence coefficient is also the confidence level. A confidence coefficient of 0.95 is the same as a confidence level of 95%.
Confidence level is used to express how confident we are that the population mean lies within the calculated confidence interval. It expresses the possibility of getting the same result if tests are repeated. Since the study reports that college students work, on average, between 4.63 and 12.63 hours a week, with confidence coefficient .95, then the true statement is
G. We are 95% confident that the population mean time that college students work is between 4.63 and 12.63 hours a week.
Give the numerical value of the parameter p in the following binomial distribution scenario.
The probability of winning an arcade game is 0.632 and the probability of losing is 0.368. If you play the arcade game 10 times, we want to know the probability of winning no more than 8 times.
Consider winning as a success in the binomial distribution. Do not include p= in your answer.
Answer:0.9306
Step-by-step explanation:
Given
Probability of winning [tex]p=0.632[/tex]
Probability of losing [tex]q=0.368[/tex]
Such that [tex]p+q=1[/tex]
Applying binomioal distribution for n=10 trials
Probability of winning no more than 8 time=P
[tex]P(r\leq 8)+P(r>8)=1[/tex]
[tex]P(r\leq 8)=1-P(r>8)[/tex]
[tex]P(r\leq 8)=1-^{10}C_9(p)^9(q)-^{10}C_{10}(p)^{10}(q)^0[/tex]
[tex]P(r\leq 8)=1-^{10}C_9(0.632)^9(0.368)-^{10}C_{10}(0.632)^{10}(0.368)^0[/tex]
[tex]P=P(r\leq 8)=0.9306[/tex]
Ben's employer will reimburse him $0.13 per mile driven. If Ben drives 210.1 miles on a business trip, what is his mileage reimbursement?
Answer:
27.31
Step-by-step explanation:
Take the number of miles and multiply by the reimbursement rate
210.1 * .13
27.313
Round to the nearest cent
27.31
Insect Weights Consider a dataset giving the adult weight of species of insects. Most species of insects weigh less than 5 grams, but there are a few species that weigh a great deal, including the largest insect known: the rare and endangered Giant Weta from New Zealand, which can weigh as much as 71 grams. Is the shape of the distribution symmetric, skewed to the right, or skewed to the left
Answer:
Step-by-step explanation:
71 grams would definitely be an outlier on the high side, whereas "most" species would weigh much less. Thus, the graph of this distribution of weights would be skewed towards the lower side, that is, to the left.
The skewness of a dataset is a measure of deviation of a random variable from the normal distribution.
The shape of the distribution is skewed to the right
From the question, we understand that:
Most of the species are less than 5 grams.One specie weighs 71 grams71 is a very large dataset, compared to the other weight of the species.
This means that
71 is an outlier of the dataset.The dataset is concentrated at the left (less than 5)When there are much data at the left of a distribution, then the distribution is positively skewed.
Hence, the shape of the is skewed to the right
See attachment for illustration of skewness of a distribution.
Read more about skewness at
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Before reporting the results of the survival analysis, the investigators compared baseline characteristics of the 38 people who withdrew from the study before its end to those who had complete follow up. this was done for which of the following reason?a. To test whether randomization was successful
b. To check for changes in prognosis over time
c. To check whether those who remained in the study represent the total study population
d. To determine whether the outcome of those who remained in the study is the same as the outcome of the underlying population
e. To check for confounders in the exposed and nonexposed groups
Answer:
the answer is D.
Step-by-step explanation:
If you go out to eat with 3 friends and your meal was $72.50, there is a 6.75% sales tax and you should tip the waiter 15%. How much should each person pay?
1)Tax $???
2)Total meal cost $???
3)Tip $???
4)Total cost of meal with tip $???
5)Price per person $???
Answer:
5 CAUSE ITS PER PERSON
x/x+1-1/x-1+2x/x^2-1
Answer:
Input:
x/x + 1 - 1/x - 1 + 2×x/x^2 - 1
Result:
1/x
c^2 = a^2 + b^2 - 2ab cos C make cos C the subject of the formula
Answer:
[tex]\frac{c^{2}-a^{2}-b^{2} }{-2ab}[/tex]=cos C
Step-by-step explanation:
Start with the parts that are more loosely attached to the cos C: the a² and the b², they are only attached with addition, which can be easily undone by subtracting from both sides. That gives you c²-a²-b²=-2abC
Next, since you want to isolate cosC, you will want to divide by everything attached to the cosC by multiplication: (c²-a²-b²)÷(-2ab)=cosC. Then you can neaten it up and put it in fraction form: [tex]\frac{c^{2}-a^{2}-b^{2} }{-2ab}[/tex]=cos C
Suppose that Motorola uses the normal distribution to determine the probability of defects and the number of defects in a particular production process. Assume that the production process manufactures items with a mean weight of 10 ounces. Calculate the probability of a defect and the suspected number of defects for a 1,000-unit production run in the following situations.
(a) The process standard deviation is 0.15, and the process control is set at plus or minus one standard deviation. Units with weights less than 9.85 or greater than 10.15 ounces will be classified as defects. If required, round your answer to four decimal places.
(b) Through process design improvements, the process standard deviation can be reduced to 0.05. Assume that the process control remains the same, with weights less than 9.85 or greater than 10.15 ounces being classified as defects. If required, round your answer to four decimal places.
(c) What is the advantage of reducing process variation, thereby causing process control limits to be at a greater number of standard deviations from the mean?
Answer:
[tex]\mathbf{P(X < 9.85 \ or \ X> 10.15) \approx 0.3171}[/tex] to four decimal places.
[tex]\mathbf{P(X < 9.85 \ or \ X> 10.15) =0.0027}[/tex] to four decimal places.
Step-by-step explanation:
a)
Assuming X to be the random variable which replace the amount of defectives and follows standard normal distribution whose mean (μ) is 10 ounces and standard deviation (σ) is 0.15
The values of the random variable differ from mean by ± 1 \such that the values are either greater than (10+ 0.15) or less than (10-0.15)
= 10.15 or 9.85.
The probability that the amount of defectives which are either greater than 10.15 or less than 9.85 can be calculated as follows:
[tex]P(X < 9.85 \ or \ X> 10.15) = 1-P ( \dfrac{9.85-10}{0.15}< \dfrac{X-10}{0.15}< \dfrac{10.15-10}{0.15})[/tex]
[tex]P(X < 9.85 \ or \ X> 10.15) = 1- \phi (1) - \phi (-1)[/tex]
Using the Excel Formula ( = NORMDIST (1) ) to calculate for the value of z =1 and -1 ;we have: 0.841345 and 0.158655 respectively
[tex]P(X < 9.85 \ or \ X> 10.15) = 1- (0.841345-0.158655)[/tex]
[tex]P(X < 9.85 \ or \ X> 10.15) =0.31731[/tex]
[tex]\mathbf{P(X < 9.85 \ or \ X> 10.15) \approx 0.3171}[/tex] to four decimal places.
b) Through process design improvements, the process standard deviation can be reduced to 0.05.
The probability that the amount of defectives which are either greater than 10.15 or less than 9.85 can be calculated as follows:
[tex]P(X < 9.85 \ or \ X> 10.15) = 1-P ( \dfrac{9.85-10}{0.05}< \dfrac{X-10}{0.05}< \dfrac{10.15-10}{0.05})[/tex]
[tex]P(X < 9.85 \ or \ X> 10.15) = 1- \phi (3) - \phi (-3)[/tex]
Using the Excel Formula ( = NORMDIST (3) ) to calculate for the value of z =3 and -3 ;we have: 0.99865 and 0.00135 respectively
[tex]P(X < 9.85 \ or \ X> 10.15) = 1- (0.99865-0.00135)[/tex]
[tex]\mathbf{P(X < 9.85 \ or \ X> 10.15) =0.0027}[/tex] to four decimal places.
(c) What is the advantage of reducing process variation, thereby causing process control limits to be at a greater number of standard deviations from the mean?
The main advantage of reducing the process variation is that the chance of getting the defecting item will be reduced as we can see from the reduction which takes place from a to b from above.
All equilateral triangles are also isosceles triangles.
Answer:
True
Step-by-step explanation:
Isosceles triangles are a subset of equilateral triangles
Equilateral have all three sides the same while isosceles have at least 2 sides the same
Equilateral have all three angles equal while isosceles have at least 2 angles equal
Answer:
Yes
Step-by-step explanation:
An equilateral triangle is one where all three sides are of equal length. (3)
An isosceles triangle has at least two sides of equal length. (2)
But, if it's the other way around than no
The difference between an ostrich's speed and a chicken's speed
is 31 miles per hour. An ostrich can run at a speed of 40 miles
per hour. Use mental math or the guess, check, and revise strategy
to solve the equation 40 – c= 31 to find c, the speed a chicken
can run.
Answer:
9 miles an hour
Step-by-step explanation:
9
N
2) A sample of size n= 49 is obtained. The population mean
is m= 80 and the population standard deviation is s = 14.
Find the probability that the sample has a sample average
between 78.3 and 85.1, (5 points)
-
Answer:
0.7969
Step-by-step explanation:
Given that: A sample of size n= 49 is obtained. The population mean is m= 80 and the population standard deviation is s = 14.
The z score measures the number of standard deviation by which the raw sore is above or below the mean. It is given by the equation:
[tex]z=\frac{x-m}{\frac{s}{\sqrt{n} } }[/tex]
For x = 78.3, the z score is:
[tex]z=\frac{x-m}{\frac{s}{\sqrt{n} } }=\frac{78.3-80}{\frac{14}{\sqrt{49} } } =-0.85[/tex]
For x = 85.1, the z score is:
[tex]z=\frac{x-m}{\frac{s}{\sqrt{n} } }=\frac{85.1-80}{\frac{14}{\sqrt{49} } } =2.55[/tex]
P(78.3<x<85.1) = P(-0.85<z<2.55) = P(z<2.55) - P(z<-0.85) = 0.9946 - 0.1977 = 0.7969
Answer:
P(78.3 < x' < 85.1) = 0.7969
Step-by-step explanation:
Given:
Sample size, n = 49
mean, u = 80
Standard deviation [tex] \sigma [/tex] = 14
Sample mean, ux' = population mean = 80
Let's find the sample standard deviation using the formula:
[tex] \sigma \bar x = \frac{\sigma}{\sqrt{n}} [/tex]
[tex] = \frac{14}{\sqrt{49}} = \frac{14}{7} = 2 [/tex]
To find the probability that the sample has a sample average between 78.3 and 85.1, we have:
[tex] P(78.3 < \bar x < 85.1) = \frac{P[(78.3 -80)}{2} < \frac{(\bar x - u \bar x)}{\sigma \bar x} < \frac{(85.1 -80)}{2}] [/tex]
= P( -0.85 < Z < 2.55 )
= P(Z < 2.55) - P(Z <-0.85 )
Using the standard normal table, we have:
= 0.9946 - 0.1977 = 0.7969
Approximately 0.80
Therefore, the probability that the sample has a sample average between 78.3 and 85.1 is 0.7969
evaluate (243/32)^-2/5*2^
-2
Answer:
1/9
Step-by-step explanation:
(243/32)^-2/5*2^ -2 = (3/2)^(5*-2/5) * 1/4 = (3/2)^-2 * 1/4 = 4/9 * 1/4 = 1/9
Please Someone help do not understand it ASAP
Answer:
1a) 90 = 2y + 2(2x) 1b) 45 - 2x = y
Step-by-step explanation:
1a) 90 = 2y + 2(2x)
1b) 90 = 2y + 2(2x) Use the equation from above and multiply
90 = 2y + 4x
-4x - 4x Subtract 4x from both sides
90 - 4x = 2y Divide both sides by 2
45 - 2x = y
Evaluate the numerical expression.
9 × [(25 − 6) − (6 + 5)]
Answer:
72
Step-by-step explanation:
9 * (19 - 11)
= 9 * 8 = 72
A researcher wishes to estimate the percentage of adults who support abolishing the penny. What size sample should be obtained if he wishes the estimate to be within 3 percentage points with 95% confidence if
(a) he uses a previous estimate of 32%?
(b) he does not use any prior estimates?
Answer:
a) [tex]n=\frac{0.32(1-0.32)}{(\frac{0.03}{1.96})^2}=928.81[/tex]
And rounded up we have that n=929
b) [tex]n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11[/tex]
And rounded up we have that n=1068
Step-by-step explanation:
Part a
The margin of error for the proportion interval is given by this formula:
[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex] (a)
And on this case we have that [tex]ME =\pm 0.03[/tex] and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex] (b)
For a confidence of 95% we have that the significance is [tex]\alpha=0.05[/tex] and the critical value would be:
[tex] z = 1.96[/tex]
And replacing into equation (b) the values from part a we got:
[tex]n=\frac{0.32(1-0.32)}{(\frac{0.03}{1.96})^2}=928.81[/tex]
And rounded up we have that n=929
Part b
For this case since we don't have prior info we can use as estimator for the true proportion the value [tex]\hat p=0.5[/tex] and replacing we got:
[tex]n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11[/tex]
And rounded up we have that n=1068
A quick quiz consists of a multiple-choice question with 3 possible answers followed by a multiple-choice question with 5 possible answers. If both questions are answered with random guesses, find the probability that both responses are correct. Report the answer as a percent rounded to one decimal place accuracy. You need not enter the "%" symbol. prob = %
Answer:
Step-by-step explanation:
I assume that there is only one right answer in each multiple-choice question
If so:
P=(1/3)*(1/5)
P=1/15
P=0.06666666666
P≈0.067
P≈6.7%
Identify J rounded to the nearest tenth. Please Explain!
Answer:
121.1
Step-by-step explanation:
By law of sines, (sin <I)/i = (sin <J)/j. Plugging in the values we know, we get sin 72deg / 206 = sin 34deg / j. When we solve for k, we get that it is about 121.122. Rounded to the nearest tenth, we get that j is 121.1.
j/k-0.02k when j=25 and k=5
Answer: 4.98
Step-by-step explanation:fractions are dividing so if j=25 and k=5 the division problem would be 25 divided by 5 then u would subtract 0.02 to get 4.98
What is the amplitude ? How do I find it? do I add -3.8 to 3.8 then divide? Thank you in advance
Answer:
7.6subtract the midline from the peak valueStep-by-step explanation:
The amplitude is the difference between the peak value (3.8) and the midline (-3.8). You find it by subtracting the midline from the peak:
amplitude = 3.8 -(-3.8)
amplitude = 7.6
These prisms have different shapes as end faces
Triangle (3 sides) 5 9 6
Rectangle (4 sides) 6 12 8
Pentagon (5 sides) 7 15 10
Hexagon (6 sides) 8 18 12
b) 300 edges and 200 vertices
(a) The complete table describes a number of faces, edges, and vertices shown below.
(b) There are 300 edges and 200 vertices in a prism with a 100-sided end face
In the given figure one is a triangular prism and the lower one is a pentagonal prism. With the help of the figure, we have to calculate the complete table and the number of edges and vertices a prism with a 100-sided end face has.
(a)
The complete table is given as:
Triangle (3 sides) 5 9 6
Rectangle (4 sides) 6 12 8
Pentagon (5 sides) 7 15 10
Hexagon (6 sides) 8 18 12
(b)
The number of vertices in a prism is determined by the number of vertices on its base polygon. Therefore, there are 300 edges and 200 vertices in a prism with a 100-sided end face.
Learn more about polygons here:
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You spin a spinner that has 15 equal-sized sections numbered 1 to 15. Find the theoretical probability of: P(odd number)
Answer: The correct answer is
Step-by-step explanation:
The probability of P(odd number) for odd numbers is 8/15
What is probability?Probability is a branch of mathematics that deals with the occurrence of a random event. For example, when a coin is tossed in the air, the possible outcomes are Head and Tail.
According to question
A spinner that has 15 equal-sized sections numbered 1 to 15.
Total number of selection = 15
therefore odd no's are = 1,3,5,7,9,11,13,15 in total 8
And even no's are = 2,4,6,8,10,12,14 in total 7
Now probability of: P(odd number) = [tex]\frac{Total odd no's }{Total number of selection}[/tex]
= 8/15
Hence, the probability of odd number is 8/15
To know more about probability here :
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# SPJ2
A dead body was found within a closed room of a house where the temperature was a constant 65° F. At the time of discovery the core temperature of the body was determined to be 80° F. One hour later a second measurement showed that the core temperature of the body was 75° F. Assume that the time of death corresponds to t = 0 and that the core temperature at that time was 98.6° F. Determine how many hours elapsed before the body was found. [Hint: Let t1 > 0 denote the time that the body was discovered.] (Round your answer to one decimal place.) hr Need Help? Read It Talk to a Tutor
Answer: 0.7 hours has elapsed before the body was found
Step-by-step explanation:
Please see the attachments below
17. El precio de los terrenos en Lima es proporcional al área e inversamente proporcional a su distancia con respecto al centro de la ciudad. Un empresario desea adquirir un terreno de 1200 m2 para instalar una pequeña planta procesadora que este localizada a una distancia máxima de 40 Km del centro de la ciudad. Si se sabe que un terreno de 900 m2 a 45 Km del centro de la ciudad cuesta S/ 250 000, ¿cuánto deberá pagar como mínimo dicho empresario para adquirir el terreno con las condiciones dadas?
Answer:
375000
Step-by-step explanation:
We have that in this case the following proportion would be fulfilled:
Price * Distance / area
Now, we have that for a distance of 45 km and an area of 900 m ^ 2 the price is 250,000, now for a distance of 40 km but with an area of 1,200 m ^ 2, how would the price be, we replace:
250000 * 45/900 = P * 40/1200
12500 * 1200/40 = P
P = 375000
Which means that for these conditions the price is 375000.
POSSIBLE POINTS
A toy box contains 12 colored toys and 12 white toys. If you pick out 3 toys at random, what is the probability that they will all be white?
Answer:
12white
12 coloured
12-12=0
What is the mean of the following set of data?
{4,3,1, 6, 1,7}
Answer:
3.6666666.... and continuing
or 3.7 if you want to round
Step-by-step explanation:
To find the mean, I added all the numbers up:
4+3+1+ 6+ 1+7 = 22
Then I divided that by how many numbers there are total (6).
22/6= 3.66666.. or 3.6 with a bar symbol on top of the 6.
Thus, the answer is 3.666666...
Find the gradient of the line 2y=-6x+1 =
Answer:
A line in form of y = ax + b has the gradient a.
2y = -6x + 1
<=> y = -3x + 1/2
=> The gradient of this line: g = -3
Hope this helps!
:)
The slope represents the gradient of the line. Then the gradient of the line will be - 3.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The linear equation is given below.
2y = - 6x + 1
Convert the equation into a slope-intercept form. Then we have
2y = - 6x + 1
y = - 3x + 1/3
The slope represents the gradient of the line. Then the gradient of the line will be - 3.
More about the linear equation link is given below.
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Multiply 6.4 x 108 by 3.1 x 10-5 and leave the
answer in standard form.
Answer:
hope this.helps you
Evaluate cos0 if sin0= 5/3
Answer:
cos0 = 4/3
Step-by-step explanation:
If sin0 = 5/3 then cos0 = 4/3
Sin is opposite/hypotenuse or 5/3.
Cos is adjacent/hypotenuse or 4/3
I found 4 because of Pythagorean Theorem on the triangle, which is known as a 345 triangle.
What is 5 square root28 plus square root 63 in simplest radical form
Answer:
13√7
Step-by-step explanation:
[tex]5\sqrt{28} +\sqrt{63} =5\sqrt{2^2\cdot 7}+\sqrt{3^2\cdot 7}\\\\=5\cdot 2\sqrt{7}+3\sqrt{7}=(10+3)\sqrt{7}\\\\=\boxed{13\sqrt{7}}[/tex]
