Assume the population has a normal distribution. A sample of 25 randomly selected students Has a mean test score of 81.5 With a standard deviation of 10.2. Construct a 90% confidence interval for the mean test score.

Answers

Answer 1

Answer:

Answer:

The 90% confidence interval for the mean test score is between 77.29 and 85.71.

Step-by-step explanation:

We have the standard deviation for the sample, so we use the t-distribution to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 25 - 1 = 24

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 24 degrees of freedom(y-axis) and a confidence level of $1 - (1 - 0.9)/(2) = 0.95$ . So we have T = 2.064

The margin of error is:

$M = T(s)/(√(n)) = 2.064(10.2)/(√(25)) = 4.21$

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 81.5 - 4.21 = 77.29

The upper end of the interval is the sample mean added to M. So it is 81.5 + 4.21 = 85.71.

The 90% confidence interval for the mean test score is between 77.29 and 85.71.

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What’s the answer to this problem 3x36-(81/9-8)+16/4=

Answers

Answer:

108x - 69

Step-by-step explanation:

Reduce the numbers with greatest common divisor 9
Calculate the product
Reduce the fraction with 4
Subtract the numbers
Calculate the sum

7n+4n combine the like terms to create an equivalent expression

Answers

Answer:

11n

Step-by-step explanation:

7n+4n (factorize out n)

= n (7 + 4)

= n (11)

= 11n

Answer:

11n

Step-by-step explanation:

Combining like terms just means adding together the numbers with the same variable. 7n and 4n both have an n attached, so you would add like normal to get 7n + 4n = 11n.

Whart is 1 divided by 1/2

Answers

Answer:

The answer is 2

Step-by-step explanation:

Use a calculator.

Gloria earned a total of $810 over the summer. She earned $162 babysitting and the restfrom mowing lawns. Which bar model and solution represent x, the amount of money Gloria
earned mowing lawns?

Answers

Let x represent the amount of money Gloria earned mowing lawns.

We have been given that Gloria earned a total of $810 over the summer. She earned $162 babysitting and the rest from mowing lawns.

The total amount earned by Gloria would be amount earned from baby sitting and lawn mowing that is $x+162$ .

Now we will equate total earnings of Gloria by 810 as:

$x+162=810$

$x+162-162=810-162$

$x=648$

Therefore, Gloria earned $648 from mowing lawns.

Answer:

Gloria earned $648 from mowing lawns

Step-by-step explanation:

Which point is a solution to the inequality shown in this graph?
(0,4)
(-3,0)

Answers

(-3,0) point is a solution to the inequality shown in this graph.

What is the definition of inequality?

Inequality is a sort of equation in which the equal sign is missing. As we will see, inequality is defined as a statement regarding the relative magnitude of two claims.

There are two solutions os inequality are;

(0,4)

(-3,0)

But only one solution is given in the graph as;

(-3,0)

Hence, the (-3,0) is the point that is a solution to the inequality shown in this graph. Option B is correct.

To learn more about inequility, refer to;

brainly.com/question/20383699.

#SPJ2

Answer:

B.(-3,0)

Step-by-step explanation:

i just finished the test

Minimizing Construction Costs The management of the UNICO department store has decided to enclose a 945 ft2 area outside the building for displaying potted plants and flowers. One side will be formed by the external wall of the store, two sides will be constructed of pine boards, and the fourth side will be made of galvanized steel fencing. If the pine board fencing costs $7/running foot and the steel fencing costs $4/running foot, determine the dimensions of the enclosure that can be erected at minimum cost. (Round your answers to one decimal place.)

Answers

Answer:

Pine board side = 16.4 ft

Steel fencing side = 57.5 ft

Step-by-step explanation:

Let 'B' be the length of each side constructed of pine boards, and 'S' be the length of the side with the steel fencing, the area (A) and cost (C) functions are:

$945 = B*S\nB=(945)/(S) \nC= 4*S+7*2B\nC=4S+(13,230)/(S)$

The value of S for which the derivate of the cost function is zero, minimizes cost:

$C'=0=4+(-13,230)/(S^2)\n S=√(3,307.5) \nS=57.5 ft$

The value of B is:

$B=(945)/(57.5)\nB=16.4 \ ft$

Pine board side = 16.4 ft

Steel fencing side = 57.5 ft

Final answer:

To minimize the construction costs for the enclosure, the dimensions should be calculated using the calculus optimization technique. By incorporating the cost and area requirements into calculated equations and solving, you will find x = 2 times y. This is how you minimize the cost.

Explanation:

This problem involves the application of calculus and optimization techniques. Given that the area of the enclosure needs to be 945 ft2, and that it is adjacent to an external wall of the department store, we can infer that its shape is rectangular.

Let the width of the enclosure parallel to the department store be x (feet), and its length perpendicular to the store be y (feet). According to the area requirement, we have the equation x*y = 945 ft2.

The cost of the enclosure is the sum of the cost of the pine board fences and the steel fence. Since 2 sides are made of pine boards, and 1 side made of steel, the cost can be expressed as C = 2xy p + y s, where 'p' is the cost of pine board per foot ($7), and 's' is the cost of steel per foot ($4).

Since we are looking for the minimum cost, we derive this equation and set it equal to zero to find the dimensions x and y. After substituting and simplifying, we find that the minimum cost is obtained when x = 2 y. By substituting this into the area equation, we can solve for the dimensions of the enclosure.