Someone please help me I’ll give out brainliest please don’t answer if you don’t know

A high school principal wishes to estimate how well his students are doing in math. Using 40 randomly chosen tests, he finds tha

ollegr [7]

Answer:

99% confidence interval for the population proportion of passing test scores is [0.5986 , 0.9414].

Step-by-step explanation:

We are given that a high school principal wishes to estimate how well his students are doing in math.

Using 40 randomly chosen tests, he finds that 77% of them received a passing grade.

Firstly, the pivotal quantity for 99% confidence interval for the population proportion is given by;

P.Q. = $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion of students received a passing grade = 77%

n = sample of tests = 40

p = population proportion

<em>Here for constructing 99% confidence interval we have used One-sample z proportion test statistics.</em>

So, 99% confidence interval for the population proportion, p is ;

P(-2.5758 < N(0,1) < 2.5758) = 0.99 {As the critical value of z at 0.5%

level of significance are -2.5758 & 2.5758}

P(-2.5758 < $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < 2.5758) = 0.99

P( $-2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < ${\hat p-p}$ < $2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.99

P( $\hat p-2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < p < $\hat p+2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.99

<u>99% confidence interval for p</u> = [ $\hat p-2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ , $\hat p+2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ]

= [ $0.77-2.5758 \times {\sqrt{\frac{0.77(1-0.77)}{40} } }$ , $0.77+2.5758 \times {\sqrt{\frac{0.77(1-0.77)}{40} } }$ ]

= [0.5986 , 0.9414]

Therefore, 99% confidence interval for the population proportion of passing test scores is [0.5986 , 0.9414].

Lower bound of interval = 0.5986

Upper bound of interval = 0.9414

6 0

3 years ago

What does the line 2x-3y=7 look like

fenix001 [56]

2x-3y=7
-3y = -2x+7
y= 2x/3-7/3
slope of 2/3 (rise 2, run 3)
y-intercept of -7/3
Would be a positive line, starting low on left and rising towards right

4 0

3 years ago

Hey guys this is really in hard what is 1-5=

Amiraneli [1.4K]

Answer:

-4

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

The length of one side of a square is (x + 2 1/4). If the perimeter is 14 units, what is the area?

Stels [109]

The perimeter is the total of adding all of the side lengths together.

A square has 4 equal side lengths.

So the perimeter of a square is:

P = s + s + s + s or P = 4s

[P = perimeter s = side lengths of the square]

Since you know the side length of the square is (x + 2 1/4), you can replace s with (x + 2 1/4)

P = 4s

P = 4(x + 2 1/4) Multiply 4 into (x + 2 1/4)

P = 4x + 8 4/4

P = 4x + 9

Since you know the perimeter, you can plug it in.(you could have also plugged it in in the beginning)

P = 4x + 9

14 = 4x + 9 Subtract 9 on both sides

5 = 4x Divide 4 on both sides

5/4 = x

Now that you know x, find the side length of the square.

(x + 2 1/4)

(5/4 + 2 1/4)

2 6/4 = 3 2/4 = 3 1/2 units or 3.5 units

To find the area of a square, you multiply 2 of the sides together:

A = s · s

A = 3.5 · 3.5

A = 12.25 units²

7 0

3 years ago

The wind force f on a sail varies jointly as the area a of the sail and the square of the wind speed w.

blondinia [14]

Answer:

122.5 lbs

Step-by-step explanation:

The relation between force, wind speed, and area can be written ...

f = ks²a

for some wind speed s and area a.

__

The constant of proportionality, k, can be found from the given data.

64.8 = k(18²)(500) . . . force in pounds, area in square feet, speed in mph

k = 64.8/(324×500) = 0.0004

__

Using the equation with the second set of data, we have ...

f = 0.0004(35²)(250) = 122.5 . . . . pounds

The force on the 250 square foot sail would be 122.5 pounds.

4 0

2 years ago