Answer:
7. μ=204.9 and σ=5.4968
8. μ=75.9 and σ=0.7136
9. p=0.9452
Step-by-step explanation:
7. - Given that the population mean =204.9 and the standard deviation is 81.90 and the sample size n=222.
-The sample mean,[tex]\mu_x[/tex]is calculated as:
[tex]\mu_x=\mu=204.9, \mu_x=sample \ mean[/tex]
-The standard deviation,[tex]\sigma_x[/tex] is calculated as:
[tex]\sigma_x=\frac{\sigma}{\sqrt{n}}\\\\=\frac{81.9}{\sqrt{222}}\\\\=5.4968[/tex]
8. For a random variable X.
-Given a X's population mean is 75.9, standard deviation is 9.6 and a sample size of 181
-#The sample mean,[tex]\mu_x[/tex] is calculated as:
[tex]\mu_x=\mu\\\\=75.9[/tex]
#The sample standard deviation is calculated as follows:
[tex]\sigma_x=\frac{\sigma}{\sqrt{n}}\\\\=\frac{9.6}{\sqrt{181}}\\\\=0.7136[/tex]
9. Given the population mean, μ=135.7 and σ=88 and n=59
#We calculate the sample mean;
[tex]\mu_x=\mu=135.7[/tex]
#Sample standard deviation:
[tex]\sigma_x=\frac{\sigma}{\sqrt{n}}\\\\=\frac{88}{\sqrt{59}}\\\\=11.4566[/tex]
#The sample size, n=59 is at least 30, so we apply Central Limit Theorem:
[tex]P(\bar X>117.4)=P(Z>\frac{117.4-\mu_{\bar x}}{\sigma_x})\\\\=P(Z>\frac{117.4-135.7}{11.4566})\\\\=P(Z>-1.5973)\\\\=1-0.05480 \\\\=0.9452[/tex]
Hence, the probability of a random sample's mean being greater than 117.4 is 0.9452
A trade magazine routinely checks the drive-through service times of fast-food restaurants. Upper A 95% confidence interval that results from examining 745 customers in one fast-food chain's drive-through has a lower bound of 177.6 seconds and an upper bound of 181.0 seconds. What does this mean?
Answer:
-A person can be 95% confident that the mean drive through service time lies between 177.6 seconds and 181.0 seconds.
Step-by-step explanation:
- Confidence level is the degree of certainty we have on a particular statistic.
-The 95% confidence interval means that we are 95% confident that the mean drive through service time is lies between 177.6 seconds and 181.0 minutes.
Graph y=4x-9 ill give brainliest for first one that is correct
Answer:
I hope this helps
Determine whether the random variable is discrete or continuous. In each case, state the possible values of the random variable. (a) The number of points scored during a basketball game. (b) The amount of rain in City Upper B during April.
Answer:
a) Discrete, because the number of point scored during basket ball is countable.
For instance, the amount of point scored in a basketball could be 75, 103, 63 etc. The numbers are countable
b) Continuous, because the amounts of rainfall is a random variable that is uncountable.
For instance, the amount of rainfall in City Upper B during April could be 0.10 inches of rain per hour, 0.30 inches of rain per hour. This numbers are not countable, they are rather approximated or rounded off.
Step-by-step explanation:
A random variable is considered discrete if its possible values are countable while a random variable is considered to be continuous if it's possible values are not countable.
Determine whether the function is even, odd, or neither. Then determine whether the function's graph is symmetric with respect to the y-axis, the origin, or neither. f(x)equals=4 x squared plus x Superscript 4 Baseline plus 3
The function f(x) = 4x2 + x4 + 3 is even because the substitution of (-x) for x results in the original function. It's not odd because replacing (-x) for x doesn't give the negative of the original function. Hence, as an even function, its graph is symmetric with respect to the y-axis.
Explanation:The function f(x) = 4x2 + x4 + 3 can be tested for symmetry. If a function is even, its graph is symmetric with respect to the y-axis. If a function is odd, its graph is symmetric with respect to the origin.
To test if a function is even, we substitute (-x) for x in the function and simplify. If the result is the original function, then the function is even. For the given function, f(-x) = 4(-x)2 + (-x)4 + 3 = 4x2 + x4 + 3. So, the function is even.
To test if a function is odd, we also substitute (-x) for x in the function and simplify. If the result is the negative of the original function, then the function is odd. In our case, f(-x) is not the negative of f(x), so the function is not odd.
Therefore, the function is even and its graph is symmetric with respect to the y-axis.
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Toilet Training You are a great friend and are taking your friend's child to the playground to play with two of his friends: Charles and Elizabeth. You overhear the dads of Charles and Elizabeth talking about a recent study regarding toilet training of children. The study found that the mean age for girls to stay dry during the day (successful completion of toilet training) is 32.5 months, and the mean age for boys is 35.0 months. These two groups had reported standard deviations for the age when a child is successfully toilet trained of 6.7 months for girls and 10.1 months for boys based on a sample of 126 girls and a second sample of 141 boys. Charles's dad and Elizabeth's dad are getting into a disagreement about how to interpret these results. Based on your knowledge from Stats 250, can you help settle their disagreement by helping to answer the following questions about the difference between the population mean age for girls to be successfully toilet trained and the population mean age for boys to be successfully toilet trained? Question 5 Subquestions 5.
a TBD points Based on our given information, should you use the unpooled (Welch's) or the pooled approach to calculate the confidence interval? Make sure to include numerical support for your answer. No answer entered. Click above to enter an answer. 5.
b TBD points The reported 95% confidence interval is (0.3927 months. 4.6073 months). Based on this confidence interval, which group was chosen to be group 1? How do you know? What is the probability that our parameter of interest, the true difference in population means of ages of successful toilet training between boys and girls, is included in the interval? No answer entered. Click above to enter an answer. 5.
C TBD points Charles's dad is upset that this result guarantees that his son will be at a disadvantage, since he will be toilet trained later than Elizabeth. Elizabeth's dad starts to correct him, stating that this only means that there is only a 95% probability that Elizabeth will be toilet trained before Charles. Are either of these statements correct? Explain why you made your choice.
Answer:
Step-by-step explanation:
Hello!
According to a study regarding the average age of female and male kids to complete toilet training is:
Females:
Average age 32.5 months
The standard deviation of 6.7 months
n= 126
Males:
Average age 35.0 months
The standard deviation of 10.1 months
n= 141
The parameter of study is the difference between the age of females are successfully toilet trained and the average age that males are successfully toilet trained. μf - μm (f= female and m= male)
a.
Assuming that both variables have a normal distribution to choose whether you'll use an unpooled or pooled-t to calculate the confidence interval you have to conduct an F-test for variance homogeneity.
If the variances are equal, then you can usee the pooled-t, but if the variances are different, you have to uses Wlche's approach:
H₀: δ²f = δ²m
H₁: δ²f ≠ δ²m
Since both items b. and c. ask for a 95% CI I'll use the complementary significance level for this test:
α: 0.05
[tex]F= \frac{S^2_f}{S^2_m} * \frac{xSigma^2_f}{Sigma^2_m} ~~~F_{(n_f-1); (n_m-1)}[/tex]
[tex]F= \frac{(6.7^2)}{(10.1)^2} *1= 0.44[/tex]
Critical values:
[tex]F_{125;140;0.025}= 0.71\\F_{125;140;0.975}= 1.41[/tex]
The calculated F value is less than the lower critical value, 0.77, so the decision is to reject the null hypothesis. In other words, there is no significant evidence to conclude the population variances of the age kids are toilet trained to be equal. You should use Welch's approach to construct the Confidence Intervals.
[tex]Df_w= \frac{(\frac{S^2_f}{n_f} + \frac{S^2_m}{n_m} )^2}{\frac{(\frac{S^2_f}{n_f} )^2}{n_f-1} +\frac{(\frac{S^2_m}{n_m} )^2}{n_m-1} }[/tex]
[tex]Df_w= \frac{(\frac{6.7^2}{126} + \frac{10.1^2_m}{141} )^2}{\frac{(\frac{126^2}{126} )^2}{126-1} +\frac{(\frac{10.1^2}{141} )^2}{141-1} } = 254.32[/tex]
b.
The given interval is:
[0.3627; 4.6073]
Using Welch's approach, the formula for the CI is:
(X[bar]f- X[bar]m) ± [tex]t_{Df_w;1-\alpha /2}[/tex] * [tex]\sqrt{\frac{S^2_f}{n_f} +\frac{S^2_m}{n_m} }[/tex]
or
(X[bar]m- X[bar]f) ± [tex]t_{Df_w;1-\alpha /2}[/tex] * [tex]\sqrt{\frac{S^2_f}{n_f} +\frac{S^2_m}{n_m} }[/tex]
As you can see either way you calculate the interval, it is centered in the difference between the two sample means, so you can clear the value of that difference by:
(Upper bond - Lower bond)/2= (4.6073-0.3627)/2= 2.1223
The average age for females is 32.5 months and for males, it is 35 months.
Since the difference between the sample means is positive, we can say that the boys were considered "group 1" and the girls were considered "group 2"
You have a95% confidence that the parameter of interest is included in the given confidence interval.
c.
None of the statements is correct, the interval gives you information about the difference between the average age the kids are toilet trained, that is between the expected ages for the entire population of male and female babies.
This represents a guideline but is not necessarily true to all individuals of the population since some male babies can be toilet trained before that is expected as some female babies can be toiled trained after the average value.
I hope it helps!
A random sample of 35 bags yielded a confidence interval for the number of calories per bag of 128.2 to 139.8 calories. Is there evidence that the nutrition label does not provide an accurate measure of calories in the bags of potato chips?
Answer:
As Null hypothesis is not satisfied so there is no evident that nutrition label doesn't provide accurate measure of calories.
Answer:
Yes
Step-by-step explanation:
Complete question is:
The nutrition label on a bag of potato chips says that a one ounce(28g) serving of potato chips has 130 calories and contains 10 grams of fats with 3 grams of saturated fats. A random sample of 35 bags yielded a confidence interval for the number of calories per bag of 128.2 to 139.8 calories. Is there evidence that the nutrition label does not provide an accurate measure of calories in the bags of potato chips?
The calories stated in nutriton label (130) is close to the lower bound of confidence interval range which is 128.2. So this can be an evidence that nutrition lable may not provide an accurate measure of calories in bags.
Lucia hit a golf ball 240 feet. How many yards did she hit the ball?
A) 80 yards
B) 60 yards
C) 120 yards
D) 300 yards
Answer:
a
Step-by-step explanation:
a yard is 3 feet.24/3 equals 8 .then 80!
evaluate tan( – 33pi/4)
Answer:??
Step-by-step explanation:
Answer: dont have an answer
Step-by-step explanation:
sorry
In a recent survey, 18 people preferred milk, 29 people preferred coffee, and 13 people preferred juice as their primary drink for breakfast. If a person is selected at random, find the probability that the person preferred milk as his or her primary drink.
Answer:
Probability that the person preferred milk as his or her primary drink = 0.3
Step-by-step explanation:
Given -
In a recent survey, 18 people preferred milk, 29 people preferred coffee, and 13 people preferred juice as their primary drink for breakfast .
Total no of people is = 18 + 29 + 13 = 60
If a person is selected at random ,
The probability of person preferred milk = [tex]\frac{18}{60}[/tex]
The probability of person preferred coffee = [tex]\frac{29}{60}[/tex]
The probability of person preferred juice = [tex]\frac{13}{60}[/tex]
Probability that the person preferred milk as his or her primary drink =
P ( milk ) = [tex]\mathbf{\frac{No\;of\;favourable\;outcomes}{total\;no\;of\:outcomes}}[/tex]
= [tex]\frac{18}{60}[/tex] = 0.3
Which statements are correct? Check all that apply.
A quadratic function can have two irrational roots.
A quadratic equation can have no real number solutions.
If a quadratic function has two real roots, then both roots must be rational.
A quadratic function can have three zeros.
All quadratic functions touch or cross the x-axis at least once.
Answer:
A quadratic function can have two irrational roots.
A quadratic equation can have no real number solutions.
Step-by-step explanation:
A quadratic function can have two irrational roots.
A quadratic equation can have no real number solutions.
What is quadratic function?A quadratic function is a polynomial function with one or more in which highest exponent of variable is two.
According to the question,
A quadratic function can have two irrational roots.
example: [tex]x^{2} -2x -2 =0[/tex]
This equation have two irrational roots 1+√3 and 1 - √3.
A quadratic function can have no real number solutions
Hence, A quadratic function can have two irrational roots.
A quadratic equation can have no real number solutions.
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Solve the system of linear equations using elimination.
−9x − 10y = 17
−10x − 10y = 10
Answer:
you are to subtract the equation
Answer:
(7,-8)
Step-by-step explanation:
HVAC technician average salary = $28/hour with a one-year Tech school certification costing an average of $7,500. What would your pay be for your first year of work? Assume you work a 40 hour week for 50 weeks.
Answer:
56,000
Step-by-step explanation:
In your first year of work, you would make $56,000.
The pay rate is $28 per hour and a work week has 40 hours for the HVAC technician.
In a week, you will make:
= Number of hours in week x Amount per hour
= 40 x 28
= $1,120
In a year, assuming there are 50 weeks, the HVAC technician would make:
= Amount per week x Number of weeks in year
= 1,120 x 50
= $56,000
In conclusion, you would make $56,000 a year as an HVAC technician.
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A market survey shows that half the owners of Sorey State Boogie Boards became disenchanted with the product and switched to C&T Super Professional Boards the next surf season, while the other half remained loyal to Sorey State. On the other hand, three quarters of the C&T Boogie Board users remained loyal to C&T, while the rest switched to Sorey State. Set these data up as a Markov transition matrix.
(Let 1 = Sorey State, and 2 = C&T.)
Answer:
[tex]\left[\begin{array}{ccc}\dfrac{1}{2} &\dfrac{1}{2}\\\\\dfrac{1}{4}&\dfrac{3}{4}\end{array}\right][/tex]
Step-by-step explanation:
Let 1 = Sorey State, and 2 = C&T
Half the owners of Sorey State Boogie Boards became disenchanted with the product and switched to C&T Super Professional Boards the next surf season.
This means half moved from State 1 to State 2.Three quarters of the C&T Boogie Board users remained loyal to C&T, while the rest switched to Sorey State.
The rest [tex](1-\frac{3}{4}= \frac{1}{4})[/tex] moved from State 2 to State 1.The Markov Transition Matrix is presented below:
[tex]\left\begin{array}{ccc}\\\\\\$Sorey State&1\\\\C\&T&2\end{array}\right\left[\begin{array}{ccc}$Sorey State&C\&T\\1&2\\------&------\\\dfrac{1}{2} &\dfrac{1}{2}\\\\\dfrac{1}{4}&\dfrac{3}{4}\end{array}\right][/tex]
The above is presented for clarity sake. The transition matrix is:
[tex]\left[\begin{array}{ccc}\dfrac{1}{2} &\dfrac{1}{2}\\\\\dfrac{1}{4}&\dfrac{3}{4}\end{array}\right][/tex]
The Markov transition matrix, based on the given question, would look as follows: The top row represents the switch from Sorey State to C&T (0.5) and C&T to Sorey State (0.25). The bottom row represents the loyal customers who stick with their Sorey State (0.5) and C&T (0.75) boards. This matrix represents the probability of customers transitioning between these two brands in one surf season.
Explanation:
To properly answer this question, we need to convert these figures into a Markov transition matrix. In a Markov transition model, each consumer either stays with the brand they have (represented by the numbers on the diagonals) or switches to the other brand (represented by the numbers not on the diagonals).
Given the problem, set it up as follows:
Half, or 0.5, of the Sorey State Boogie Boards customers transitioned to C&T, this means that 0.5 of those customers stayed with Sorey State.Alternatively, one quarter, or 0.25, of the C&T customers transitioned to Sorey State, meaning that 0.75 of them remained with C&T.As a matrix, this looks as follows:
[Sorey State, C&T Boards]
[0.5, 0.25]
[ 0.5, 0.75]
This is your completed Markov transition matrix, which represents the probability of customers transitioning between these two brands, from one surf season to the next.
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given: f(x)= x^2 -x and g(x)= x+2 find f(-1)
Consider the following linear programming problem: The feasible corner points are (48,84), (0,120), (0,0), (90,0). What is the maximum possible value for the objective function
Answer:
We have,
max 4x+10y
3x+4y<480
4x+2y<360
The feasible corner points are ( 48,84),(0,120),(0,0),(90,0)
Now, our problem is maximum type so put above feasible points in equation max 4x + 10y one by one and select one point at which our value from this equation is maximum,
(48,84) 4*48+10*84 1032
(0,120) 4*0+10*120 1200
(0,0) 4*0+10*0 0
(90,0) 4*90+10*0 360
Here we get maximum value at (0,120) which is 1200.
Correct option is (B)1200
Answer:
Answer is 1200.
Refer below.
Step-by-step explanation:
The maximum possible value for the objective function is 1200.
identify the horizontal aysmptote of each graph. t(x)=6^x
Answer:Y=0 Y=-3
Step-by-step explanation:
Answer:
First graph y=0
Second graph y=-3
Step-by-step explanation:
Edge 2022
Help me please I'm in 6th grade
Answer:
1271.7 cm3
Step-by-step explanation:
Answer:
1,271.7cm
Step-by-step explanation:
V=π*r^2 * (h/3)
V= 3.14 * 9^2 * (15/3)
V= 3.14 * 81 * 5 =1271.7
.
Write an equation for the line that is parallel to the given line and that passes through the given point. y=−6x+2;(−1,2)
A. y=−8x−8y=-8x-8
B. y=6x−8y=6x-8
C. y=−6x+4y=-6x+4
D. y=−6x−4y=-6x-4
complete the equation of the line whose slope is -2 and y intercept is (0,3)
Answer:
y = -2x+3
Step-by-step explanation:
Answer:
We have to produce the equation y = mx +b
We start by solving for b
b = y - mx
b = 3 - -2*0
b = 3
Let's put b and the slope into this equation
y = mx +b
y = -2*x +3
Step-by-step explanation:
Look at the cahrt below The number of satisfied customers is given below each month on the x axis select an appropriate scale for the y axis of the graph
Answer:
wydjae is męi ze tak
Step-by-step explanation:
The appropriate scale for the y-axis include:
A = 2000
B = 4000
C = 6000
D = 8000
E = 10000
F = 12000
G = 14000
In Mathematics and Euclidean Geometry, a bar chart is a type of graph that is used for the graphical representation of a data set, especially through the use of rectangular bars and vertical columns.
Since the set of axes starts from the origin (0, 0), an appropriate scale for the y-axis (number of satisfied customers) of the graph can be calculated as follows;
1 unit = 250 customers
4 units = (4 × 250) = 2,000 customers.
In this context, the appropriate scale for the y-axis should be completed as follows:
A = 2000
B = 4000
C = 6000
D = 8000
E = 10000
F = 12000
G = 14000
Complete Question;
Look at chart below.
The number of satisfied customers is given below each month on the x-axis.
Select an appropriate scale for the y-axis of the graph.
The appropriate scale for the y-axis is:
A =
B =
C =
D =
E =
F =
G =
Given that M=(2 0 6 3 7), then the order of the matrix M is
Answer:
63720
Step-by-step explanation:
yes
It takes Ernesto 3 minutes to jog a lap around the school track. How many laps can Ernesto complete in 15 minutes?
Answer:
5 laps
Step-by-step explanation:
We can use ratios to solve
3 minutes 15 minutes
----------------- = ------------------------
1 lap x laps
Using cross products
3x = 15
Divide each side by 3
3x/3 = 15/3
x = 5
He can do 5 laps
plz help!!!!
You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately p∗=73%. You would like to be 90% confident that your esimate is within 4% of the true population proportion. How large of a sample size is required
Answer:
Ans: n = [1.645/0.02]^2*0.13*0.87 = 766 when rounded up
Step-by-step explanation:
How can you use a point on the graph off-1(x) =
9X to determine a point on the graph of f(x) =
logox?
Answer: switch the x- and y- coordinates
And the 2nd part is c, e , f
The point on the graph -1(x) =9X to determine a point on the graph of f(x) =logox is (-1, -9).
How to know if a point lies in the graph of a function?All the points (and only those points) which lie on the graph of the function satisfy its equation.
Thus, if a point lies on the graph of a function, then it must also satisfy the function.
We are given that;
-1(x) =9X
Now,
To use a point on the graph of one function to determine a point on the graph of another function, you need to find the corresponding x-value on the first graph. Then, you can use that x-value to find the corresponding y-value on the second graph.
In this case, you have a point on the graph of the function f(x) = 9x. To find the corresponding point on the graph of the function g(x) = log(x), you need to find the x-value that corresponds to -1 on the graph of f(x) = 9x.
To do this, you can set f(x) = 9x equal to -1 and solve for x:
9x = -1 x = -1/9
The point (-1, -9) on the graph of f(x) = 9x corresponds to the point (-1/9, log(-1/9)) on the graph of g(x) = log(x). However, note that the logarithm function is not defined for negative values of x, so the point (-1/9, log(-1/9)) is not a valid point on the graph of g(x) = log(x).
Therefore, by the graph of function the point will be (-1, -9).
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A rectangular bin is going to be made with a volume of 646 cm^3. The base of the bin will be a square and the top will be open. The cost of the material for the base is 0.5 cents per square centimeter, and the cost of the material for the sides is 0.3 cents per square centimeter. Determine the dimensions of the bin that will minimize the cost of manufacturing it. What is the minimum cost?
Answer:
The base is a square of side 9.19 cm and the height is 7.66 cm
[tex]C_m=126.58\ cents[/tex]
Step-by-step explanation:
Optimization
We'll use simple techniques to find the optimum values that minimize the cost function given in the problem. Since the restriction is an equality, the derivative will come handy to find the critical points and then we'll prove they are a minimum.
First, we consider the shape of the rectangular bin has a square base and no top. Let x be the side of the base, thus the Area of the base is
[tex]A_b=x^2[/tex]
Let y be the height of the box, thus each one of the four lateral sides of the box is a rectangle with sides x and y and the total lateral area is
[tex]A_s=4xy[/tex]
The cost of the material used to manufacture the box is 0.5 cents per square centimeter of the base and 0.3 cents per square centimeter of the sides, thus the total cost to produce one box is
[tex]C(x,y)=0.5x^2+0.3\cdot 4xy[/tex]
[tex]C(x,y)=0.5x^2+1.2xy[/tex]
Note the cost is a two-variable function. We need to have it expressed as a single variable function. To achieve that, we use the volume provided as [tex]646 cm^3[/tex]. The volume of the box is the base times the height
[tex]V=x^2y[/tex]
Using the value of the volume we have
[tex]x^2y=646[/tex]
Solving for y
[tex]\displaystyle y=\frac{646}{x^2}[/tex]
Replacing into the cost function, it only depends on one variable
[tex]\displaystyle C(x)=0.5x^2+1.2x\cdot \frac{646}{x^2}[/tex]
Operating
[tex]\displaystyle C(x)=0.5x^2+ \frac{775.2}{x}[/tex]
Taking the first derivative
[tex]\displaystyle C'(x)=x-\frac{775.2}{x^2}[/tex]
Equating to 0
[tex]\displaystyle x-\frac{775.2}{x^2}=0[/tex]
Solving
[tex]\displaystyle x=\sqrt[3]{775.2}[/tex]
[tex]x=9.19\ cm[/tex]
Now find the height
[tex]\displaystyle y=\frac{646}{9.19^2}[/tex]
[tex]y=7.66\ cm[/tex]
Find the second derivative
[tex]\displaystyle C''(x)=1+\frac{1550.4}{x^3}[/tex]
Since this value is positive, for all x positive, the function has a minimum at the critical point.
Thus, the minimum cost is
[tex]\displaystyle C_m=0.5\cdot 9.19^2+ \frac{775.2}{9.19}[/tex]
[tex]\boxed{C_m=126.58\ cents}[/tex]
Answer:
126.58 cents or $1.27
Step-by-step explanation:
the math from above is correct they just want the answers in dollars
The population of a city (in millions) at time t (in years) is P(t)=2.6 e 0.005t , where t=0 is the year 2000. When will the population double from its size at t=0 ?
Answer:
year 2139
Step-by-step explanation:
The population will double when the factor e^(.005t) is 2.
e^(.005t) = 2
.005t = ln(2)
t = ln(2)/0.005 = 138.6
The population will be double its size at t=0 when t=138.6. That is the population will be about 5.2 million in the year 2139.
The population will double by the year 2139 from its value of 2.6 million in year 2000.
Population function :
[tex]P(t) = 2.6 {e}^{0.005t} [/tex]
Population size at t = 0
[tex]P(0) = 2.6 {e}^{0.005(0)} = 2.6(1) = 2.6[/tex]
Population at t = 2.6 million.
For the population to double ;
2.6 × 2 = 5.2 million :
[tex]5.2 = 2.6 {e}^{0.005t} [/tex]
We solve for t
[tex] \frac{5.2}{2.6} = {e}^{0.005t} [/tex]
[tex]2 = {e}^{0.005t} [/tex]
Take the In of both sides
[tex] ln(2) = 0.005t[/tex]
[tex]t \: = ln(2) \div 0.005 = 138.629[/tex]
The population will double after 139 years
Therefore, the population will double by the 2139 (Year 2000 + 139 years) = year 2139.
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Cars arrive randomly at a tollbooth at a rate of 20 cars per 10 minutes during rush hour. What is the probability that exactly five cars will arrive over a five-minute interval during rush hour?
Answer:
3.78% probability that exactly five cars will arrive over a five-minute interval during rush hour
Step-by-step explanation:
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 time interval.
20 cars per 10 minutes
So for 5 minutes, [tex]\mu = 10[/tex]
What is the probability that exactly five cars will arrive over a five-minute interval during rush hour?
This is P(X = 5).
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 5) = \frac{e^{-10}*(10)^{5}}{(5)!} = 0.0378[/tex]
3.78% probability that exactly five cars will arrive over a five-minute interval during rush hour
The probability that exactly five cars will arrive over a five-minute interval during rush hour is approximately 0.0378 or 3.78%.
Firstly, the arrival rate is given as 20 cars per 10 minutes. Thus, the arrival rate per minute, λ, is 20 cars / 10 minutes = 2 cars per minute. To find the arrival rate for a 5-minute interval, we multiply this rate by 5 minutes: λ = 2 cars/minute * 5 minutes = 10 cars.
The Poisson probability formula is:
P(X = k) = (λ^k * e^(-λ)) / k!
where λ is the average number of cars in the interval, k is the number of cars, and e is the base of the natural logarithm (approximately equal to 2.71828).
In this problem, we need to find the probability of exactly 5 cars arriving in a 5-minute interval. Thus, λ = 10 and k = 5:
P(X = 5) = (10^5 * e^(-10)) / 5!
P(X = 5) = (100000 * e^(-10)) / 120
P(X = 5) ≈ (100000 / 148.4132) / 120
P(X = 5) ≈ 0.0378
Therefore, the probability that exactly five cars will arrive over a five-minute interval during rush hour is approximately 0.0378 or 3.78%.
In a survey conducted by the Gallup Organization, 1100 adult Americans were asked how many hours they worked in the previous week. Based on the results, a 95% confidence interval for the mean number of hours worked had a lower bound of 42.7 and an upper bound of 44.5. Provide two recommendations for decreasing the margin of error of the interval.
Answer:
1) Increase the sample size
2) Decrease the confidence level
Step-by-step explanation:
The 95% confidence interval built for a sample size of 1100 adult Americans on how much they worked in previous week is:
42.7 to 44.5
We have to provide 2 recommendations on how to decrease the margin of Error. Margin of error is calculated as:
[tex]M.E=z_{\frac{\alpha}{2} } \times \frac{\sigma}{\sqrt{n}}[/tex]
Here,
[tex]z_{\frac{\alpha}{2} }[/tex] is the critical z-value which depends on the confidence level. Higher the confidence level, higher will be the value of critical z and vice versa.
[tex]\sigma[/tex] is the population standard deviation, which will be a constant term and n is the sample size. Since n is in the denominator, increasing the value of n will decrease the value of Margin of Error.
Therefore, the 2 recommendations to decrease the Margin of error for the given case are:
Increase the sample size and make it more than 1100Decrease the confidence level and make it lesser than 95%.The two recommendations should be that the sample size should be increased and the confidence interval should be reduced.
Suggestions for reducing the margin of error:Since a 95% confidence interval for the mean number of hours worked had a lower bound of 42.7 and an upper bound of 44.5.
We know that margin of error = z value × population / √n
So for reducing the margin of error of the interval, sample size should be increased and the confidence interval should be reduced.
Learn more about mean here: https://brainly.com/question/20875379
a sweater is marked 30% off during an end of the season sale. if the sweater was orginally 56.00, how much was the sweater on sale for
Answer:
39.20000
Step-by-step explanation:
Sweater costs 56.00
To calculate the discounted price of the sweater
56 * (30/100) = 16.8
We used (30/100) to find out the 30 percent of the sweater which will be on discount/reduced.
56-16.8=39.2 is the discounted price
Then we subtract the amount of discount from the original price of sweater to find out the discounted price.
American Statistical Association budget is distributed normally with a mean spending of $45.67 and a standard deviation of $5.50. What is the probability that the spending is more than $42.35
Answer:
Probability that the spending is more than $42.35 is 0.7271.
Step-by-step explanation:
We are given that American Statistical Association budget is distributed normally with a mean spending of $45.67 and a standard deviation of $5.50.
Let X = American Statistical Association budget
So, X ~ N([tex]\mu=45.67,\sigma^{2} =5.5^{2}[/tex])
The z-score probability distribution for normal distribution is given by;
Z = [tex]\frac{ X -\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = mean spending = $45.67
[tex]\sigma[/tex] = standard deviation = $5.50
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) 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.
So, the probability that the spending is more than $42.35 is given by = P(X > $42.35)
P(X > $42.35) = P( [tex]\frac{ X -\mu}{\sigma}[/tex] > [tex]\frac{42.35-45.67}{5.5}[/tex] ) = P(Z > -0.604) = P(Z < 0.604)
= 0.7271
Now, in the z table the P(Z [tex]\leq[/tex] x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 0.604 in the z table which will lie between x = 0.60 and x = 0.70 which has an area of 0.7271.
Hence, the probability that the spending is more than $42.35 is 0.7271.