Given that IQ is normally distributed with a mean of 100 and a standard deviation of 15 and the sample size, n=16
We need to find the probability that a randomly selected sample has a mean greater than 105.
The z-score is given by;[tex]z = \frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}\[/tex]
The sample mean of size n=16 is [tex]\bar{x}=105[/tex], the population mean is [tex]\mu=100[/tex] and the standard deviation is [tex]\sigma=15[/tex]. Now we need to find the probability that the z-score is greater than z. Since the sample size is greater than 30, we can use the z-distribution to approximate the standard normal distribution. Since the sample size is n=16 which is less than 30, we cannot use the z-distribution to approximate the standard normal distribution. Instead, we use the t-distribution, which is a set of distributions that are similar to the standard normal distribution but are dependent on the sample size. The formula for the t-score is given by;
[tex]t=\frac{\bar{x}-\mu}{\frac{s}{\sqrt{n}}}\[/tex]Where [tex]s[/tex] is the sample standard deviation. Since the population standard deviation is unknown, we use the sample standard deviation instead.
The sample mean of size n=16 is [tex]\bar{x}=105[/tex],
the population mean is [tex]\mu=100[/tex],
the sample standard deviation is [tex]s=\frac{\sigma}{\sqrt{n}}=\frac{15}{\sqrt{16}}=3.75[/tex].
The t-score is given by[tex]t=\frac{105-100}{\frac{3.75}{\sqrt{16}}}=4.267\[/tex]
The degrees of freedom is given by n-1 = 16-1 = 15. Using the t-table with 15 degrees of freedom and a two-tailed test at the 0.05 level of significance, the critical value is 2.131. Since the t-score is greater than the critical value, we reject the null hypothesis and conclude that there is sufficient evidence to suggest that the sample mean is greater than the population mean. The p-value is the area under the curve to the right of the t-score. We find the p-value using the t-table. The p-value is 0.0002. Hence, the probability that a randomly selected sample has a mean greater than 105 is 0.0002 (or 0.02%). Therefore, the option with the correct answer is 0.0002.
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Cody did not understand the concepts of the “special cases” when factoring. Explain the concept of the perfect square binomial. Use an example to help explain to her how it is a special case and how to factor it using the special case rules.
A binomial expression of the form (a + b)² or (a - b)² is called a perfect square binomial.
This expression can be factored using the special case rules by rewriting it in the form
(a + b)(a + b) or (a - b)(a - b), respectively.
A perfect square binomial is a quadratic trinomial in which the first term is a perfect square and the second term is twice the product of the square root of the first term and the square root of the last term.
In the context of special cases, the perfect square binomial is a binomial that is formed by squaring a binomial.
This is a special case because it has a unique factorization, as we will see later.
An example of a perfect square binomial is (x + 4)².
This is because the first term, x², is a perfect square, and the second term, 8x, is twice the product of the square root of x² and the square root of 4, which is 2.
Hence, (x + 4)² can be factored using the special case rules as:
(x + 4)(x + 4),
which simplifies to
(x + 4)².
A perfect square binomial is a quadratic trinomial in which the first term is a perfect square and the second term is twice the product of the square root of the first term and the square root of the last term.
It is a special case because it has a unique factorization, which is given by the formula:
(a + b)² = a² + 2ab + b²
or
(a - b)² = a² - 2ab + b².
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Rewrite as an addition equation and determine the answer: -3 - - 8 =
Answer:
-3 + 8 = 5
Step-by-step explanation:
When we have a "minus a negative", it's a positive. So the - -8 is the same as + 8.
LMK if you have questions.
-3 + -8 = -11
is that a nice one or something
PLEASE ANSWERS FAST
how do you find the perimeter of the base?
A. Multiply the side lengths
B. Divide the side lengths
C. Add all sides of the base shape
D. Take the square root after multiplying the side lengths
Answer:
C. Add all sides of the base shape
Step-by-step explanation:
perimeter = sum of length of sides of a polygon
Answer: C. Add all sides of the base shape
need help plz im struggling
Answer:
12057.6
Step-by-step explanation:
V = πr²h
3.14 x 16² x 15
3.14 x 16² = 803.843.14 x 803.84 = 12057.6Test whether there is a difference in the pattern of freshman class ranks (an ordinal scale variable) of the newly-inducted sophomore members across five sororities at Mega University.
The required answer is by conducting the Kruskal-Wallis test, we can determine if there are statistically significant differences in the pattern of freshman class ranks among the sophomore members across the five sororities at Mega University.
To test whether there is a difference in the pattern of freshman class ranks among the sophomore members across five sororities at Mega University, we can use a statistical test called the Kruskal-Wallis test. The Kruskal-Wallis test is a non-parametric test used to compare the distributions of three or more independent groups.
In this case, the five sororities represent the independent groups, and the freshman class ranks of the sophomore members within each sorority are the ordinal scale variable of interest. The Kruskal-Wallis test will assess whether there are statistically significant differences in the distribution of freshman class ranks across the five sororities.
Here is a step-by-step explanation of how to conduct the Kruskal-Wallis test:
Step 1: Formulate the null and alternative hypotheses.
Null hypothesis (H₀): There is no difference in the pattern of freshman class ranks across the five sororities.
Alternative hypothesis (H₁): There is a difference in the pattern of freshman class ranks across the five sororities.
Step 2: Collect the data.
Gather the freshman class ranks of the sophomore members for each sorority. Ensure that the data is properly coded and organized.
Step 3: Perform the Kruskal-Wallis test.
Apply the Kruskal-Wallis test to the data. The test will compare the distributions of the ordinal data across the five sororities and determine if there are significant differences.
Step 4: Interpret the results.
Analyze the output of the Kruskal-Wallis test, which typically provides a test statistic and a p-value. If the p-value is below a predetermined significance level (e.g., 0.05), we reject the null hypothesis and conclude that there is evidence of a difference in the pattern of freshman class ranks across the five sororities.
Step 5: Post-hoc analysis (if necessary).
If the Kruskal-Wallis test indicates significant differences, further analyses, such as pairwise comparisons or Dunn's test, can be conducted to identify which specific sororities differ from each other.
By conducting the Kruskal-Wallis test, we can determine if there are statistically significant differences in the pattern of freshman class ranks among the sophomore members across the five sororities at Mega University.
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Find the area of the figure.
Answer:
353.93 ft²
Step-by-step explanation:
Step 1:
Find the area of the Trapezoid.
(a + b) ÷ 2 × height
20 + 17 = 37
37 ÷ 2 = 18.5
18.5 × 13 = 240.5 ft²
Step 2:
Find the Area of the Semicircle:
1/2 × πr²
1/2 × 3.14 = 1.57
1.57 × 8.5² = 113.43 ft²
Step 3:
Add the two areas together:
240.5 + 113.43 = 353.93 ft²
Which solution for z makes the equation true?? 10+10+z=40=10 (pls explain why. Thanks)
Answer:
z=30
Step-by-step explanation:
40-10=30
10+10+?=30
30-10-10=10
I'm sorry cuz I don't know how to explain it
Answer:
z = 10
Step-by-step explanation:
10 + 10 + z = 40 - 10
10 + 10 + z = 30
10 + 10 + 10 = 30
since 40 - 10 = 30, then Z has to equal 10 because 10 + 10 + z needs to be 30
(z^6/z)^2 QUICK ILL GIVE BRANLIEST
Answer, z10
Step-by-step explanation:
2. (1 point each) Let f(x) = √x and g(x) = 1/x. In the space
provided, compute each of the following, if possible:
(a) f(36)
(b) (g+f)(4)
(c) (f · g)(0)
(a) f(36) is equal to 6.
(b) (g+f)(4) = g(4) + f(4) = 9/4
(c) we cannot compute (f · g)(0).
(a) To find f(36), we substitute x = 36 into the function f(x) = √x:
f(36) = √36 = 6
Therefore, f(36) is equal to 6.
(b) To find (g+f)(4), we need to evaluate g(4) and f(4), and then add the results:
g(4) = 1/4
f(4) = √4 = 2
(g+f)(4) = g(4) + f(4) = 1/4 + 2 = 1/4 + 8/4 = 9/4
Therefore, (g+f)(4) is equal to 9/4 or 2.25.
(c) To find (f · g)(0), we need to evaluate f(0) and g(0), and then multiply the results:
f(0) = √0 = 0
g(0) = 1/0
However, g(0) is undefined because division by zero is not defined in mathematics.
Therefore, we cannot compute (f · g)(0) in this case.
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Thomas has finished 50% of an art project that has taken him a total of 9 hours so far. If he continues to work at the same rate, how many hours will it take for him to complete the entire project?
Answer:
18 hours
Step-by-step explanation:
9/0.50 = 18 hours
Can someone help me out please.
Answer:
area = (10 x 19) - (0.5 x 19 x 5) = 142.5 in²
Step-by-step explanation:
Answer:
142.5 in^2
Step-by-step explanation:
Area of trapezoid= a + b / 2 · h (a and b are bases of the trapezoid)
A= 5 + 10 / 2 · 19
A= 15 / 2 · 19
A= 7.5 · 19
A= 142.5 in^2
This is just one way to do it. There are many more ways.
Find the sum of the interior angle measures of the polygon.
Answer:
360
Step-by-step explanation:
All the angles of a polygon add up to 360, thats kinda just how it is haha
if the third term is 20 and 7th is 1.25, find the 11th term
Answer:
the 11th term is 0.0000488 or 4.88*10^-5.
Step-by-step explanation:
a3 = 20, a7 = 1.25
a7 = a3r^7-3
1.25 = 20r^4
r^4 = 0.0625
r = 4th root of 0.0625
r = 0.5
a3 = a1r^3-1
20 = a1(20)^2
400a1 = 20
a1 = 0.05
a11 = 0.05(0.5)^11-1 = 0.0000488 or 4.88*10^-5
help║...................
3 questions
4 is about what percent of 9?
About what percent of 7560 is 3000?
1.3 is about what percent of 27?
Please help me my teacher does not explain how to do this well..
please help with right answers xoxo
On Saturday, a local hamburger shop sold a combined total of 261 hamburgers and cheeseburgers. The number of cheeseburgers sold was two times the number of hamburgers sold. How many hamburgers were sold on Saturday?
Answer:
134 hamburgers
Step-by-step explanation:
Let H = # of hamburgers
# of cheeseburgers = 2H
H + 2H = 402
3H = 402
H = 402/3
H = 134
Let V be the set of all ordered triples of real numbers with addition and scalar multiplication defined as follows: (x, y, z) + (x'. y' z') = (x + x'.0,2 + z!) and k(x,y,z) (kx,ky, kz) for all real numbers k. Prove that V is not a vector space.
The set V, defined as the set of all ordered triples of real numbers with the given addition and scalar multiplication operations, is not a vector space. Therefore, we can conclude that V is not a vector space, as it does not fulfill the required vector space axioms.
To prove that V is not a vector space, we need to demonstrate that it fails to satisfy at least one of the vector space axioms.
Let's consider the closure under scalar multiplication axiom. According to the given scalar multiplication operation, k(x, y, z) = (kx, ky, kz) for all real numbers k. However, in a vector space, scalar multiplication should be distributive over both addition of vectors and scalar addition.
Let's choose a specific example to illustrate the issue. Consider the vector (x, y, z) = (1, 1, 1) in V and the scalar k = 2. According to the defined scalar multiplication operation, 2(x, y, z) = 2(1, 1, 1) = (2, 2, 2).
Now, let's compute (1 + 1)(x, y, z) = 2(x, y, z) = 2(1, 1, 1) = (2, 2, 2).
However, in a vector space, the distributive property should hold, meaning that (1 + 1)(x, y, z) should equal (1, 1, 1) + (1, 1, 1) = (2, 2, 2).
Since (1 + 1)(x, y, z) ≠ (1, 1, 1) + (1, 1, 1), V fails to satisfy the closure under scalar multiplication axiom.
Therefore, we can conclude that V is not a vector space, as it does not fulfill the required vector space axioms.
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Roads connecting the towns of Oceanside, River City, and Lake View form a triangle. The distance from Oceanside to River City is 38 kilometers. The distance from River City to Lake View is 26 kilometers. What is the smallest possible whole number of kilometers between Lake View and Oceanside?
Answer:
13 km
Step-by-step explanation:
By Triangle Inequality Theorem: The sum of two smallest sides is greater than the third side.
Small Values of X:
X + 26 > 38
X > 38 - 26
X > 12
If we know that 38 km is the longest side, then the sum of other two sides must be greater than 38 km. Therefore the minimum value of X is 13 km.
Which of the following is the correct alternative hypothesis constructed in the binomial test? A. H, :P Previous question
The correct alternative hypothesis constructed in a binomial test is (a) H₁ :P < Q
How to determine the correct alternative hypothesis constructed in a binomial test?From the question, we have the following parameters that can be used in our computation:
A. H₁ :P < Q
B. H₁: P - Q
C. H₁ : P = Q
D. H₁ : P ≤ Q
As a general rule of test of hypothesis, alternate hypothesis are represented using inequalities
This means that we make use of <, > or ≠
Hence, the correct alternative hypothesis is (a) H₁ :P < Q
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Question
Which of the following is the correct alternative hypothesis constructed in the binomial test?
A. H₁ :P < Q
B. H₁: P - Q
C. H₁ : P = Q
D. H₁ : P ≤ Q
Please Help, GodBless
Answer:
-3/2
Step-by-step explanation:
The rate of change is the same as slope
20 POINTS‼️‼️Which of the following does NOT represent the number of months in a year?
A and b are in the attached photo.
C. y= 12x, where x represents the number of years and y represents the number of months
D. There are 96 months in 8 years.
‼️PLEASE DO YOUR BEST TO SHOW WORK FOR BRAINLIEST‼️
Answer:
B because when you multiply the first number by twelve the first two are correct but the second ones are not
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
12 times 6 = 72, not 60
Find the distance between (5, -1) and (1,-5).
4 units I assume. that it is a very basic answer tho and I am not sure if a specific formula or lesson was supposed to be applied to that andwer
Find the distance between the points (–10,3) and (–2,3).
Answer:
8
Step-by-step explanation:
10 - 2
help ASAP! Ill mark brainliest!
Answer:
55 students
Step-by-step explanation:
Just write down the answer.
Answer:
Step-by-step explanation:
Football: 500(.38)= 190
Basketball: 500(.25)= 125
55 students (65 students)
I need help on this question and answering it
Answer:
75 feet
Step-by-step explanation:
the shadow to the object would be a 4:5 ratio
since the shadow of the flagpole is 60 ft,
4x=60 so x would =15
then you multiply 15 by 5 and end up with 75
Answer: 75 feet
Step-by-step explanation: trust me
Refer to Exhibit 6-6. What percentage of tires will have a life of 34,000 to 46,000 miles? a. 38.49% b. 76.98% c. 50% d. None of the alternative answers is correct
The percentage of tires will have a life of 34,000 to 46,000 miles is the correct answer is d. None of the alternative answers is correct.
The provided percentages do not offer a precise estimate of the proportion of tires with a life of 34,000 to 46,000 miles.
Determining the percentage of tires falling within a specific mileage range requires access to accurate statistical data from tire manufacturers or comprehensive studies. Several factors affect tire lifespan, such as driving habits, road conditions, maintenance, and the type of tire itself.
These variables make it difficult to provide an exact percentage without specific information about the tire population in question. To obtain a more accurate estimate, it would be necessary to analyze relevant data, such as tire industry reports or studies on tire longevity.
Tire manufacturers often provide estimated mileage ratings for their products, but these figures are averages and can vary depending on the factors mentioned above.
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What is the volume of a cone with a radius 3 cm and a height 6 cm?
Answer:
56.55
Step-by-step explanation:
Complete the table below for the equation y=1+2x
Which of these describe a unique polygon
Answer: d
Step-by-step explanation: