Answer:
a) 50.41% probability that neither will need repair.
b) 8.41% probability that both will need repair.
c) 49.59% probability that at least one car will need repair.
Step-by-step explanation:
For each car, there are only two possible outcomes. Either it will need repairs, or it will not need repairs. The probability of a car needing repairs is independent of other cars. So we use the binomial probability distribution to solve this question.
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.
17% of cars will need to be repaired once, 10% will need repairs twice, and 2% will require three or more repairs.
This means that [tex]p = 0.17+0.1+0.02 = 0.29[/tex]
Two cars:
This means that [tex]n = 2[/tex]
a) neither will need repair?
This is P(X = 0).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{2,0}.(0.29)^{0}.(0.71)^{2} = 0.5041[/tex]
50.41% probability that neither will need repair.
b) both will need repair?
This is P(X = 2).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{2,2}.(0.29)^{2}.(0.71)^{0} = 0.0841[/tex]
8.41% probability that both will need repair.
c) at least one car will need repair?
Either none will need repair, or at least one will. The sum of these probabilities is 100%.
From a)
50.41% probability that neither will need repair.
p = 100 - 50.41 = 49.59%
49.59% probability that at least one car will need repair.
Which of the following functions will only lie in the third quadrant?
y = 2 − 3
y = − − 4
None of the above.
Both A and B.
b.
If it's a (+,+) it's the 1st quadrant. If it's a (-,+) it's the 2nd quadrant. If its a (-,-) it's the 3rd quadrant. And if it's a (+,-) it's the 4th quadrant
Answer:
B
Step-by-step explanation:
Please help I can’t fail after all the hard work I have put in
Answer:180cm^2
Step-by-step explanation:
A1=25×20=500
A2=16×20=320
A1-A2
500-320=180
The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 44 ounces and a standard deviation of 10 ounces. Use the Empirical Rule. Suggestion: sketch the distribution in order to answer these questions. a) 95% of the widget weights lie between 34 and 54 b) What percentage of the widget weights lie between 34 and 64 ounces
Answer:
a) No 95% of values will fall between (24;64); 68,27% will fall between (34;54)
b)71,83 % will fall between 34 and 64 ounces
Step-by-step explanation:
Empirical rule establishes, for a normal distribution with mean μ and σ as standard deviation:
In interval μ ± σ or ( μ + σ ; μ - σ) we should find 68.27 % of all values of the population, and by simmetry 68.27/2 = 34,14 % should be over the mean and the other half would be values below the mean
Therefore in our case
μ + σ = 44 + 10 = 54
And
μ - σ = 44 - 10 = 34
a) Then 68,34 % of values will fall in this interval
We know now that value 34 is 1* σ below the mean, and is at the limit of 34,14 %
b) μ + 2*σ = 44 * 2*10 = 44 + 20 = 64
64 is the upper limit for the interval μ + 2*σ and we know that 95.45 % of all values will fall between ( μ - 2*σ ; μ + 2*σ ) and by simmetry just one side of this interval (the right side ) will have 95.45/2 = 47;73 %
Then in interval going from ( 34 ; 64 ) we shoud find 47.73 + 34,14
71,83 % of all values will fall between 34 and 64
Given YZ tangent to J at point Y, and the mWYZ =104 what is the mWXY
Answer:
152
Step-by-step explanation:
[tex]m \angle {WYZ}=104[/tex] is given, and the angle next to it is a supplement. (Unfortunately, that angle can't be named in the usual way because there is no labeled point "southeast" of point Y.)
That angle has measure 180 - 104 = 76.
Now arc WXY's measure is twice the measure of this angle, so mWXY = 2(76) = 152.
Answer:
152
Step-by-step explanation:
A kite is 3 feet long. How many inches is that?
Answer:
36 inches
Step-by-step explanation:
1 foot is equal to 12 inches so if the kite is 3 feet you would multiply 12 times 3 and get 36 hope this helps (Brainliest???)
The kite is 36 inches long. This is because 1 foot is equivalent to 12 inches, and the kite is 3 feet long.
Explanation:The question asks how many inches long is a kite that is 3 feet long. We know that 1 foot is equal to 12 inches. Therefore, to get the length of the kite in inches, we need to multiply 3 feet by 12. So, 3 feet is equal to 36 inches.
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The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took the customers in the sample to check out was 3.1 minutes. The population standard deviation is known to be 0.5 minutes. We want to test to determine whether or not the mean waiting time of all customers is significantly different than 3 minutes. Use α = 0.05.
A) The test statistic is ___________.
i. 1.96
ii. 1.64
iii. 2.00
iv. 0.056
Answer:
iii. 2.00
Step-by-step explanation:
Our test statistic is:
[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the population mean(the mean we are testing), [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
We are testing a mean of 3 times.
This means that [tex]\mu = 3[/tex]
The average length of time it took the customers in the sample to check out was 3.1 minutes. The population standard deviation is known to be 0.5 minutes. Sample of 100.
So [tex]X = 3.1, \sigma = 0.5, n = 100[/tex]
[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]t = \frac{3.1 - 3}{\frac{0.5}{\sqrt{100}}}[/tex]
[tex]t = 2[/tex]
So the correct answer is:
iii. 2.00
In ΔIJK, the measure of ∠K=90°, KJ = 63, IK = 16, and JI = 65. What ratio represents the sine of ∠I?
Answer: The sine of ∠I is represented by the ratio 63:65
Step-by-step explanation:
First, let's draw the triangle (see the picture below.)
Remember SOHCAHTOA? We need to use it here.
-sin = opposite/hypotenuse
-cos = adjacent/hypotenuse
-tan = opposite/adjacent.
Assuming that ∠I is Ф, we can see that its opposite side is equal to 63 and the hypotenuse is 65. Therefore,
[tex]sin = \frac{63}{65}[/tex]
The sine ratio is 63: 65.
What is Trigonometry?The area of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and abbreviations.
Given:
∠K=90°, KJ = 63, IK = 16, and JI = 65.
Using Sine Ratio
sin [tex]\theta[/tex] = opposite/hypotenuse
sin [tex]\theta[/tex] = 63/65
Hence, the sine ratio is 63: 65.
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Solve the equation for the unknown quantity.
6y + 7 = 5y - 7
y= (Simplify your answer.)
Answer:
y = -14 in simplest form hope this helped
Step-by-step explanation:
(−8k+1)(−8k+1) standard form
Answer:
64k^2 - 16k +1
Step-by-step explanation:
We can rewrite this as
(-8k+1) ^2
We know that (a+b)^2 = a^2 +2ab +b^2
Let a = -8k and b = 1
(-8k+1) = (-8k)^2 +2*(-8k)(1) + 1^2
=64k^2 - 16k +1
Answer:
64k² - 16k + 1
Step-by-step explanation:
(−8k+1)(−8k+1)
64k² - 8k - 8k + 1
64k² - 16k + 1
How much is 1.7÷.01 (step-by-step)
Answer:
170
Step-by-step explanation:
Hello!
Let's represent a decimal as a fraction. That will help.
Since division is multiplication by the reciprocal, we can represent 0.01 as 1/100 which will be 100 when we divide.
1.7 * 100 = 170.0 (when we move one spot over.)
Thus, we see that [tex]\boxed{170}[/tex] is the answer.
Hope this helps!
Ms. Bridges asked her class to evaluate the expression she wrote on her whiteboard.
5 x (4+6) - 9
What is the solution to the expression?
Answer:
41
Step-by-step explanation:
PEMDAS parentheses equation multiplication division adding subtraction
v
Next
Graphs of Quadratic Relationships: Mastery Test
Select the correct answer.
if y(t) = |(5-), which statement is true?
A.
The graph of function fis stretched vertically by a scale factor of 3 to create the graph of function g.
B. The graph of function fis stretched horizontally by a scale factor of 3 to create the graph of function g.
C. The graph of function fis compressed horizontally by a scale factor of to create the graph of function g.
D. The graph of function fis compressed vertically by a scale factor of to create the graph of function g.
Reset
Reset
Next
Answer:c
Step-by-step explanation:
The expression of the translated function g(x) is gotten as; g(x) = 2x² - 3
Here, we have,
to Interpret Graph Translations:
We are given the function;
f(x) = 2x² + 3
Now, when we translate a function f(x) downwards, the new function becomes;
g(x) = f(x) - a
where a is the amount of units by which the graph was translated.
Thus for translation of 6 units vertically downwards;
g(x) = 2x² + 3 - 6
g(x) = 2x² - 3
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Complete question:
The function fis defined as follows.
f(x)=2x²+3
If the graph of fis translated vertically downward by 6 units, it becomes the graph of a function g.
Find the expression for g(x).
A particular paper described a study of children who were underweight or normal weight at age 2. Children in the sample were classified according to the number of sweet drinks consumed per day and whether or not the child was overweight one year after the study began. Is there evidence of an association between whether or not children are overweight after one year and the number of sweet drinks consumed? Assume that it is reasonable to regard the sample of children in this study as representative of 2 to 3 years old children and then test the appropriate hypotheses using a .05 significance level. (Round your answer to two decimal places.)
The chi-square test shows strong evidence [tex]\left(\chi^2=93.33\right)[/tex] of an association between sweet drink consumption and children's overweight status one year later, rejecting the null hypothesis (p < 0.05).
To determine if there is a significant association between the number of sweet drinks consumed and whether or not children are overweight after one year, we can perform a chi-square test for independence. The null hypothesis ([tex]H_0[/tex]) assumes that there is no association, while the alternative hypothesis ([tex]H_a[/tex]) suggests that there is a significant association.
Let's set up the hypotheses:
[tex]H_0[/tex]: There is no association between the number of sweet drinks consumed and whether or not children are overweight after one year.[tex]H_a[/tex]: There is an association between the number of sweet drinks consumed and whether or not children are overweight after one year.We will use the chi-square test statistic to evaluate these hypotheses. The formula for the chi-square test statistic [tex]\left(\chi^2\right)[/tex] for a contingency table is given by:
[tex]\chi^2=\sum \frac{\left(O_{i j}-E_{i j}\right)^2}{E_{i j}}[/tex]
Where:
[tex]O_{ij[/tex] is the observed frequency in cell ij,
[tex]E_{ij[/tex] is the expected frequency in cell ij, which is calculated under the assumption of independence.
Let's calculate the expected frequencies and then use them to compute the chi-square test statistic.
To calculate the expected frequencies ([tex]E_{ij[/tex]), we first need to calculate the row and column totals, and the overall total.
Now, we can calculate the expected frequencies using the formula:
[tex]E_{i j}=\frac{\text { Row Total } \times \text { Column Total }}{\text { Grand Total }}[/tex]
Let's calculate [tex]E_{ij[/tex] for each cell.
Now, using the observed and expected frequencies, we can calculate the chi-square test statistic.
[tex]\chi^2=\sum \frac{\left(O_{i j}-E_{i j}\right)^2}{E_{i j}}[/tex]
After calculating this sum, we can compare the result to a chi-square distribution with degrees of freedom given by (number of rows−1)×(number of columns−1). Let's proceed with the calculations.
The chi-square test statistic [tex]\left(\chi^2\right)[/tex] is approximately 93.33. To determine the p-value and make a conclusion about the association, we need to compare this test statistic to the critical value from the chi-square distribution.
The degrees of freedom (df) for this test is (4−1) × (2−1)=3.
At a significance level of 0.05, we can look up the critical value from the chi-square distribution table with df = 3. The critical value is approximately 7.815.
Since 93.33>7.815, we reject the null hypothesis. There is evidence of a significant association between the number of sweet drinks consumed and whether or not children are overweight after one year.
Complete Question:
Applying Triangle Classification Theorems
To get from his house to the lecture hall at school, Lin
walked west 651 feet. After class, he walked northeast
910 feet to the gym. Finally, he walked 615 feet back to
his house from the gym.
What general direction did Lin walk from the gym to his
house, and what type of triangle did his walking path
form?
gym
Lin walked south, creating a right triangle.
Lin walked southwest, creating an obtuse triangle.
Lin walked southeast, creating an acute triangle.
Lin walked directly east, creating a right triangle.
910 ft
615 ft
lecture hall
651 ft Lin's house
Answer:
the correct answer is B
Step-by-step explanation:
i got it correct choosing B on the assignment ;D
The triangle formed by Lin's walking path is an acute triangle.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Lin initially walked west 651 feet from his house to the lecture hall.
After class, he walked northeast 910 feet to the gym.
Finally, he walked 615 feet back to his house.
If we draw a diagram, placing Lin's house to the left, the lecture hall to the right, and the gym above, we can see that Lin walked in a diagonal path from the gym to his house.
Since Lin initially walked west and then northeast, the resulting direction would be southeast.
Regarding the type of triangle formed by Lin's walking path, we can consider the sides and angles.
Lin walked 910 feet northeast and 615 feet back to his house.
These sides are not equal in length, indicating that it is not an equilateral triangle.
Additionally, since Lin walked southeast, the angle at the gym is acute (less than 90 degrees).
Therefore, the triangle formed by Lin's walking path is an acute triangle.
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how to factor10x^2+89x-9
Look at the attached picture ⤴
Hope it will help u...:)
When a survey asked subjects whether they would be willing to accept cuts in their standard of living to protect the environment, 387 of 1160 subjects said yes. a. Find the point estimate of the proportion of the population who would answer yes. b. Find the margin of error for a 95% confidence interval. c. Construct the 95% confidence interval for the population proportion. What do the numbers in this interval represent? d. State and check the assumptions needed for the interval in (c) to be valid.
Answer:
Step-by-step explanation:
The sample proportion is the point estimate for the population proportion.
Confidence interval is written as
Sample proportion ± margin of error
Margin of error = z × √pq/n
Where
z represents the z score corresponding to the confidence level
p = sample proportion. It also means probability of success
q = probability of failure
q = 1 - p
p = x/n
Where
n represents the number of samples
x represents the number of success
a) From the information given,
n = 1160
x = 387
p = 387/1160 = 0.33
q = 1 - 0.33 = 0.67
the point estimate of the proportion of the population who would answer yes = 0.33
b) To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.5 = 0.05
α/2 = 0.05/2 = 0.025
This is the area in each tail. Since we want the area in the middle, it becomes
1 - 0.025 = 0.975
The z score corresponding to the area on the z table is 1.96. Thus, confidence level of 95% is 1.96
Therefore,
Margin of error = 1.96√(0.33)(0.67)/1160 = 0.027
c) the 95% confidence interval for the population proportion is
0.33 ± 0.027
The numbers represent the sample proportion and the margin of error
d) The assumptions are
1) the sampling must be random
2) the sample size shouldn't be more than 10% of the population
10/100 × 1160 = 116
387 > 116
3) the sample size should be sufficiently large. That is, greater than 30
387 > 30
The point estimate is 33.4%. The margin of error for a 95% confidence interval is ±2.8%. That makes the 95% confidence interval (0.306, 0.362), and we can say with 95% confidence that the true population proportion lies within this interval. For the confidence interval to be valid, the survey must be randomized, and have at least 10 yeses and noes.
Explanation:The subject here is statistics, and it involves estimating a population proportion and calculating a margin of error and a confidence interval. The proportion of subjects who said yes is 387/1160=0.334 or 33.4%. This represents the point estimate of the proportion of the entire population who would answer yes.
For the margin of error (ME) formula for a confidence interval, we use the formula ME=Z*(sqrt[(p(1-p))/n]). For a 95% confidence interval, our Z-score is approximately 1.96. Inserting our values gives us ME=1.96*(sqrt[0.334(1-0.334)/1160])≈0.028, or 2.8%.
To calculate the 95% confidence interval, subtract and add the margin of error from the point estimate: (0.334 - 0.028, 0.334 + 0.028) or (0.306, 0.362). These numbers mean that we're 95% confident that the true population proportion who would say yes lies within this interval.
To form a valid confidence interval, we need two assumptions: a random sample and at least 10 successes and failures. The survey presumably uses a random sample. With 387 yeses and 773 noes, we satisfy the success-failure condition.
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20 footballs to 25 footballs
Answer:
4 to 5
Step-by-step explanation:
20 footballs to 25 footballs
Divide each term by 5
20/5 to 25/5
4 to 5
18 years after purchasing shares in a mutual fund for $6300, the shares are sold for $11200 what is the total return and the annual return percentage
Answer:
A = 11,600
P = 6,000
Total return = 11600-6000/6000 X 100%= 93.3%= (11600/6000) (1/17)– 1= 0.03954 * 100%= 3.954= 4.0%.
Step-by-step explanation:
The total return after 18 years in a mutual fund of $6300 is $4,900 and the annual return percentage is 77.78%.
Total Return:
Calculate the total return: $11,200 (selling price) - $6,300 (purchase price) = $4,900
Annual Return Percentage:
Annual Return Percentage = [(Final Value - Initial Value) / Initial Value] * 100
Find the percentage return: ($4,900 / $6,300) x 100%
Annual return percentage = 77.78%
What is the answer for 8b - 2b -4
Simplfied Answer: [tex]6b-4[/tex]
Combine Like Terms
[tex]8b+-2b+-4\\(8b+-2b)+(-4)\\6b+-4[/tex]
Answer:
[tex]8b - 2b - 4 \\ 6b - 4 \\ = 2(3b - 2)[/tex]
which inequality is equivalent to 5x+2(3x+1)<3? a. 10x+2<3 b. 11x+2<3 c. 10x+1<3 d. 11x+1<3
Final answer:
To find the equivalent inequality to 5x + 2(3x + 1) < 3, distribute the 2 and combine like terms, yielding 11x + 2 < 3. Thus, the answer is b. 11x + 2 < 3.
Explanation:
The question asks which inequality is equivalent to 5x + 2(3x + 1) < 3. To find the equivalent inequality, we distribute the 2 into the parentheses and combine like terms:
5x + 2(3x + 1) = 5x + (2 × 3x) + (2 × 1)5x + 6x + 2 < 3(5x + 6x) + 2 < 311x + 2 < 3Therefore, the correct answer is b. 11x + 2 < 3.
Solve the inequality 4x- 7 < 5
Answer:
x < 3
Step-by-step explanation:
Rearrange the equation by subtracting what is to the right of the greater than sign from both sides of the inequality :
4*x-7-(5)<0
Step 1 :
Pulling out like terms :
1.1 Pull out like factors :
4x - 12 = 4 • (x - 3)
Equation at the end of step 1 :
Step 2 :
2.1 Divide both sides by 4
Solve Basic Inequality :
2.2 Add 3 to both sides
x < 3
By solving the given inequality "[tex]4x-7<5[/tex]", we get the answer "[tex]x <3[/tex]". A complete solution is below.
The given equation of inequality is:
[tex]4x-7<5[/tex]Now,
By adding "7" both sides of the equation, we get
→ [tex]4x-7+7<5+7[/tex]
→ [tex]4x< 12[/tex]
→ [tex]x < \frac{12}{4}[/tex]
→ [tex]x < 3[/tex]
Thus the above solution is correct.
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If a pool measures 30 feet by 66 feet, what is the scale of the drawing shown? 1 in =
To determine the scale of a drawing, you need the dimensions on the drawing or map as well as the actual dimensions of the object. The scale is then calculated as the ratio of these two sets of dimensions. However, without the dimensions of the drawing in this case, it is not possible to determine the exact scale.
Explanation:The scale of a drawing is a ratio that compares the dimensions of the physical object to the dimensions on the drawing or map. In this case, the physical object is a pool that measures 30 feet by 66 feet. To find the scale, you would need additional information such as the dimensions of the pool in the drawing.
For example, if the pool is drawn as 2 inches by 4.4 inches on the paper, then the scale of the drawing would be 1 inch = 15 feet (for length) and 1 inch = 15 feet (for width), as 30 feet / 2 inches = 15 feet per inch and 66 feet / 4.4 inches = 15 feet per inch respectively.
Without this additional information, it is not possible to provide the exact scale of the drawing.
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The scale for the drawing shown is 1 in = 6 feets
How to determine the Scale of the drawingUsing the parameters given ;
Actual dimension :
length = 66 feets width = 30 feetsDrawing dimension :
Length = 11 feets width = 5 feetsTo calculate the scale of the drawing : Take the ratio of equivalent sides of the two drawings ;
Actual length / Drawing length = Actual width / drawing widthNow we have ;
Scale = 66 / 11 = 6Hence the scale drawing is :
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A University of Florida study on drinking habits asks a random sample of students if they drink any alcohol when they party. We want to extend the results to all students at the university. In this problem, we want to make inferences about: Group of answer choices comparing proportions from dependent samples comparing proportions from 2 independent samples one mean comparing means from dependent samples one proportion comparing means from 2 independent samples
Answer:
One proportion
Step-by-step explanation:
A proportion refers to a statement that two different ratios are equal. There are two ways It can be written: since two equal fractions a/b = c/d; or using a colon, a:b = c:d. in view of the fact that the cross products are of both equal to one hundred, we are aware that these ratios are equal and that this is a true proportion.
When making inference about a population based on a single group of subject involving proportion, then we use a one sample proportion test.
In the scenario described, only one random group of students wer sampled, hence, the result of the sampling would be a proportion of the population. Based on the inference obtained from the sample proportion, an extension of the result will be termed a one sample proportion test.Learn more : https://brainly.com/question/3565320
What is the value of u
A national sports magazine believes that 38% of Americans said they were fans of baseball. A polling company claims more Americans are fans of baseball. A random sample of 400 people indicated that 176 were baseball fans. Use a 0.01 level of significance. If testing the polling company’s claim, state the hypothesis and identify which hypothesis represents the claim.
Answer: The alternative hypothesis represents the claim
Step-by-step explanation:
We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
µ = 0.38
For the alternative hypothesis,
µ > 0.38
Considering the population proportion, probability of success, p = 0.38
q = probability of failure = 1 - p
q = 1 - 0.38 = 0.6
Considering the sample,
Sample proportion, P = x/n
Where
x = number of success = 176
n = number of samples = 400
P = 176/400 = 0.44
We would the test statistic which is the z score
z = (p - P)/√pq/n
z = (0.44 - 0.38)/√(0.38 × 0.62)/400 = 2.47
Recall, population proportion, P = 0.38
The difference between sample proportion and population proportion(P - p) is 0.44 - 0.38 = 0.06
Since the curve is symmetrical and it is a two tailed test, the p for the left tail is 0.38 - 0.06 = 0.32
the p for the right tail is 0.38 + 0.06 = 0.44
These proportions are higher and lower than the null proportion. Thus, they are evidence in favour of the alternative hypothesis. We will look at the area in both tails. Since it is showing in one tail only, we would double the area
From the normal distribution table, the area above z is 1 - 0.9932 = 0.0068
We would double this area to include the area in the left tail of z = - 2.47. Thus
p = 0.0068 × 2 = 0.014
Since alpha, 0.01 < than the p value, 0.014, then we would fail to reject the null hypothesis. Therefore, at a 1% level of significance, we do not have enough evidence to reject the null hypothesis
Compute the variation of each predicted population mean from the sample means in the table. Sample 1: Sample 2: Sample 3:
1st sample 1.5
2nd sample -2.5
3rd sample 5.5 this is the correct answers verified by the website ed
Step-by-step explanation:
Answer:
Step-by-step explanation:
Question 1: 1.5
Question 2: -2.5
Question 3: 5.5
Assume that long earlobes in humans are an autosomal dominant trait that exhibits 30% penetrance. A person who is heterozygous for long earlobes mates with a person who is homozygous for normal earlobes. What is the probability that their first child will have long earlobes (State probability as a decimal and round to the nearest hundredth i.e. 0.01 with no extra spaces)?
Answer:
0.75
Step-by-step explanation:
Autosomal dominant: A pattern of inheritance in which an affected individual has one copy of a mutant gene and one normal gene on a pair of autosomal chromosomes
Heterozygous just means that a person has two different versions of the gene (one inherited from one parent, and the other from the other parent).
Being homozygous for a particular gene means you inherited two identical versions.
The trait is autosomal dominant so the characters pass into the next generation in a large ratio. the person who is heterozygous for the character have two type of allele which represents the trait for long earlobes and also for short earlobe.So a person is paired with homozygous individuals who have pure character for short earlobes.The percentage of their first child with long earlobes would be 75 percent. This is due to the dominance of the character in a generation.
The Wisconsin Dairy Association is interested in estimating the mean weekly consumption of milk for adults over the age of 18 in that state. To do this, they have selected a random sample of 300 people from the designated population. The following results were recorded: Given this information, if the leaders wish to estimate the mean milk consumption with 90 percent confidence, what is the approximate margin of error in the estimate? Question 16 options: ±12.996 ounces ±0.75 ounce ±0.456 ounce z = 1.645
Answer:
[tex] ME = 1.653 *\frac{7.9}{\sqrt{300}}= \pm 0.75[/tex]
±0.75 ounce
Step-by-step explanation:
Assuming this complete question: The Wisconsin Dairy Association is interested in estimating the mean weekly consumption of milk for adults over the age of 18 in that state. To do this, they have selected a random sample of 300 people from the designated population. The following results were recorded: xbar=34.5 ounces, s=7.9 ounces Given this information, if the leaders wish to estimate the mean milk consumption with 90 percent confidence, what is the approximate margin of error in the estimate?
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
[tex]\bar X=34.5[/tex] represent the sample mean
[tex]\mu[/tex] population mean (variable of interest)
s=7.9 represent the sample standard deviation
n=300 represent the sample size
Solution to the problem
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
In order to calculate the critical value [tex]t_{\alpha/2}[/tex] we need to find first the degrees of freedom, given by:
[tex]df=n-1=300-1=299[/tex]
Since the Confidence is 0.90 or 90%, the value of [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.05,199)".And we see that [tex]t_{\alpha/2}=1.653[/tex]
And the margin of error is given by:
[tex] ME = 1.653 *\frac{7.9}{\sqrt{300}}= \pm 0.75[/tex]
±0.75 ounce
Answer:
The approximate margin of error in the estimate is ±0.75 ounces.
Step-by-step explanation:
The question is incomplete:
The following results were recorded: xbar=34.5 ounces, s=7.9 ounces.
The sample size is n=300.
We will use the sample standard deviation to estimate the population standard deviation, so we will use the t-statistic.
To develop a confidence interval, we first have to calculate the degrees of freedom, and then look up in a t-students distribution table the critical value for a 90% confidence interval.
The degrees of freedom are:
[tex]df=n-1=300-1=299[/tex]
The critical value for a 90% CI is t=1.65.
Now, we can calculate the margin of error of the confidence interval as:
[tex]E=t\cdot s/\sqrt{n}=1.65*7.9/\sqrt{300}=13.035/17.32=0.75[/tex]
The lower and upper bounds of the confidence interval will be:
[tex]LL=\bar x-t\cdot s/\sqrt{n}=34.5-0.75=33.75\\\\UL=\bar x+t\cdot s/\sqrt{n}=34.5+0.75=35.25[/tex]
The confidence interval is (33.75, 35.25)
A market surveyor wishes to know how many energy drinks teenagers drink each week. They want to construct a 80%80% confidence interval with an error of no more than 0.070.07. A consultant has informed them that a previous study found the mean to be 3.63.6 energy drinks per week and found the variance to be 1.441.44. What is the minimum sample size required to create the specified confidence interval? Round your answer up to the next integer.
Answer:
481
Step-by-step explanation:
Given:
Variance = 1.44
S.d = √1.44 = 1.2
C.I = 80%
Margin of error, E = 0.07
Mean = 3.6
Using Z table, the Z score for 80% confidence interval, Zc = 1.28
To find the sample size, n, we have:
[tex] n= [\frac{Z_c * s.d}{E}]^2 [/tex]
Substituting figures in the formula, we have:
[tex] n = [\frac{1.28 * 1.2}{0.07}]^2 [/tex]
n = 21.94286²
n = 481.49
Approximately, n = 481
4.1 or 4.085 greater
Answer:
4.1 >
Step-by-step explanation:
Answer:
Among 4.1 and 4.085
4.1 is greater
:))