1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
lord [1]
3 years ago
14

Suppose that scores on the mathematics part of a test for eighth-grade students follow a Normal distribution with standard devia

tion σ = 150. You want to estimate the mean score within ±20 with 90% confidence. How large an SRS of scores must you choose? (Round your answer up to the next whole number.)
Mathematics
1 answer:
riadik2000 [5.3K]3 years ago
8 0

Answer:

We need an SRS of scores of at least 153.

Step-by-step explanation:

We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\alpha = \frac{1-0.9}{2} = 0.05

Now, we have to find z in the Ztable as such z has a pvalue of 1-\alpha.

So it is z with a pvalue of 1-0.05 = 0.95, so z = 1.645

Now, find M as such

M = z*\frac{\sigma}{\sqrt{n}}

In which \sigma is the standard deviation of the population and n is the size of the sample.

How large an SRS of scores must you choose?

This is at least n, in which n is found when M = 20, \sigma = 150. So

M = z*\frac{\sigma}{\sqrt{n}}

20 = 1.645*\frac{150}{\sqrt{n}}

20\sqrt{n} = 1.645*150

\sqrt{n} = \frac{1.645*150}{20}

\sqrt{n} = 12.3375

(\sqrt{n})^{2} = (12.3375)^{2}

n = 152.2

Rounding to the next whole number, 153

We need an SRS of scores of at least 153.

You might be interested in
From a July 2019 survey of 1186 randomly selected Americans ages 18-29, it was discovered that 248 of them vaped (used an e-ciga
jasenka [17]

Answer:

The 90% confidence interval is (0.1897, 0.2285).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence interval 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

Z is the zscore that has a pvalue of 1 - \frac{\alpha}{2}

For this problem, we have that:

From a July 2019 survey of 1186 randomly selected Americans ages 18-29, it was discovered that 248 of them vaped (used an e-cigarette) in the past week. This means that n = 1186, \pi = \frac{248}{1186} = 0.2091

Construct a 90% confidence interval to estimate the population proportion of Americans age 18-29 who vaped in the past week.

So \alpha = 0.10 , z is the value of Z that has a pvalue of 1 - \frac{0.10}{2} = 0.95, so z = 1.645.

The lower limit of this interval is:

\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2091 - 1.645\sqrt{\frac{0.2091*0.7909}{1186}} = 0.1897

The upper limit of this interval is:

\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2091 + 1.645\sqrt{\frac{0.2091*0.7909}= 0.2285

The 90% confidence interval is (0.1897, 0.2285).

3 0
3 years ago
Which of the following shows that ABCD is a parallelogram for x=6 and y =8? (20 points)
Reika [66]

Answer:

AB = CD = 44 and BC = AD = 31 ; so ABCD is a parallelogram

Step-by-step explanation:

A parallelogram should have two pairs of parallel sides meaning the length of side AB should be the same as the length of side CD and the length of side AD should be the same as the length of side BC.

<u>First, lets see if line AB is parallel to line CD.</u>

Let's start by finding out the length of line AB.

Since we know x = 6 we will replace x with 6 in the expression:

7(6) + 2 = 42 + 2 = 44

Now that we know the length of line AB is 44, lets find the length of line CD by replacing x with its value of 6:

9(6) - 10 = 54 - 10 = 44

Now that we know the length of line CD is 44, we can see that line AB is parallel to line CD since they both have the same length of 44.

<u>Now, lets see if line BC is parallel to line AD.</u>

Let's start by finding out the length of line BC.

Since we know y = 8 we will replace y with 8 in the expression:

3(8) + 7 = 24 + 7 = 31

Now that we know the length of line BC is 31, lets find the length of line AD by replacing y with its value of 8:

5(8) - 9 = 40 - 9 = 31

Now that we know the length of line AD is 31, we can see that line BC is parallel to line AD since they both have the same length of 31.

<u>Conclusion</u>

ABCD is a parallelogram because it contains two parallel sides.

5 0
2 years ago
A line that intersects one of two parallel lines intersects the other also.
IceJOKER [234]

Answer:

Never

Step-by-step explanation:

It is not possible for one out of two parallel lines to be cut by a transversal, because eventually it would have to intersect

8 0
3 years ago
Tina had $15.73 • She purchased 3 plastic bracelets for $1.88 each and 1 hair ribbon for $1.23 • There was no sales tax How much
Lady_Fox [76]

Answer:

B. $8.86

Step-by-step explanation:

$1.88 * 3 plastic bracelets = $5.64

$1.23 for one hair ribbon

$5.64 + $1.23 = $6.87

$15.73 - $6.87 = $8.86

3 0
2 years ago
Read 2 more answers
A line that includes the points (-2,-7) and (-3, p) has a slope of -6. what is the value of p
MrRissso [65]

Answer:

p=-1

Step-by-step explanation:

y-y1=m(x-x1)

-7-p=-6(-2+3)

-7-p=-6

-p=1

p=-1

5 0
3 years ago
Other questions:
  • for the simple harmonic motion d = 9cos (pi//2t), what is the maximum displacement from the equilibrium position?
    12·2 answers
  • One-third of the dairy cattle on a farm are in the barn. Three-fifths of the beef cattle are in the barn. There are 30 dairy cat
    6·1 answer
  • If f(x) varies directly with x2, and f(x) = 40 when x = 2, find the value of f(5).
    6·1 answer
  • 2+2? I don’t know the answer I am in first grade
    15·2 answers
  • CORRECT ANSWER GETS 25 BRAINIEST
    6·2 answers
  • Find the degree measure of alpha to the nearest tenth of a degree.
    9·2 answers
  • An experiment was designed to measure how long subjects could track a moving target on a computer screen. The target moved errat
    15·1 answer
  • The question is find the product of -8 and the sum of -2(10x + 3y) and -5(6y -7x)
    10·2 answers
  • Help- i dont know what it is at all
    14·1 answer
  • HURRYYY i neeeeeddd helppppppppp look at the photo ^^^
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!