Will mark brainliest has to be correct.

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

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

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

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

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

= [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

For the inequality, -4x + 5 >-5

vodka [1.7K]

Answer:

x<2.5

Step-by-step explanation:

-4x +5>-5

-4x>-5-5

-4x>-10

x<10/4(on multiplying (-)ve sign both the sides inequality changes)

x < 2.5

8 0

3 years ago

HURRY HELP PLS‼️‼️‼️

Brums [2.3K]

Answer:

Step-by-step explanation:

To solve this problem you need the function

h(t) = -16t2 + v0t + h0

where t = time

v0 is the initial velocity, which in our case is 0

h0 = initial height, which in our case is 256

h(t) = 0 since we want to know when the ball will hit the ground.

0 = -16 t2 + 256

And we can solve for t

If we rearrange the terms we see that this is a difference of 2 squares

0 = 256 - 16t2

0 = (16-4t)(16+4t)

Setting each factor = 0

16-4t=0 16+4t=4

t = 4 t = -4

The second solution is discarded as time cannot be negative.

So the ball will hit the ground in 4 seconds.

6 0

3 years ago

What is the solution of the equation 3/4x +5 = -9? 16 3 Done

Licemer1 [7]

X=-56/3

multiply everything by 4 to cancel the fraction which will give you
3x+20=-36

then combine like terms to get
3x=-56

then divide to get x by itself to get

x=-56/3

since this is a weird decimal, leave it as an improper fraction

5 0

3 years ago

Write a mathematical sentence that expresses the information given below . Use t as your variable name.Necessary type <= to m

miskamm [114]

Answer:

t + 8° > 82°

Step-by-step explanation:

Given that :

Let t = temperature when Susanne checks at 11:00

If t rises by 8 more degrees, it will break the record high temperature for that day

Record high temperature for the day = 82 degree

Hence,

Temperature at 11:00 + 8° > record high temperature for the day

t + 8° > 82°

6 0

3 years ago

Will mark brainliest has to be correct. ​

Will mark brainliest has to be correct.