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
mote1985 [20]
3 years ago
8

The average heights of a random sample of 400 people from a city is 1.75 m. It is known that the heights of the population are r

andom variables that follow a normal distribution with a variance of 0.16.
Determine the interval of 95% confidence for the average heights of the population.
Mathematics
1 answer:
Dimas [21]3 years ago
4 0

Answer:

The 95% confidence interval for the average heights of the population is between 1.7108m and 1.7892m.

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{1-0.95}{2} = 0.025

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 1-0.025 = 0.975, so z = 1.96

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.

The standard deviation is the square root of the variance. So

\sigma = \sqrt{0.16} = 0.4

Then

M = 1.96*\frac{0.4}{\sqrt{400}} = 0.0392

The lower end of the interval is the mean subtracted by M. So it is 1.75 - 0.0392 = 1.7108m

The upper end of the interval is the mean added to M. So it is 1.75 + 0.0392 = 1.7892m

The 95% confidence interval for the average heights of the population is between 1.7108m and 1.7892m.

You might be interested in
What is thirty-six thousandths as a decimal
gulaghasi [49]

Answer: 0.036

Step-by-step explanation:

4 0
2 years ago
17. Solve the following:<br> x – 3y = 5<br> 5x – 2y = -1
Phantasy [73]

Answer:

(- 1, - 2 )

Step-by-step explanation:

Given the 2 equations

x - 3y = 5 → (1)

5x - 2y = - 1 → (2)

Rearrange (1) expressing x in terms of y by adding 3y to both sides

x = 5 + 3y → (3)

Substitute x = 5 + 3y in (2)

5(5 + 3y) - 2y = - 1 ← distribute left side

25 + 15y - 2y = - 1

25 + 13y = - 1 ( subtract 25 from both sides )

13y = - 26 ( divide both sides by 13 )

y = - 2

Substitute y = - 2 in (3) for corresponding value of x

x = 5 + (3 × - 2) = 5 - 6 = - 1

Solution is (- 1, - 2 )

8 0
3 years ago
Translate the following word phrase into nine times the difference of 5 and y
emmasim [6.3K]
Answer: 9 * (5 - y)

Explanation:

Times: multiplication

Difference: subtraction

y: the unknown variable
4 0
3 years ago
A men's department store sells 3 different suit jackets, 6 different shirts, 8 different ties, and 4 different pairs of pants. h
Ksenya-84 [330]
Jackets = 3
Shirt = 6
Ties = 8
Pants = 4

Number of combination = 3 x 6 x 8 x 4 = 576

Answer: There are 576 possible combinations.
3 0
3 years ago
Copy the problems onto your paper, mark the givens and prove the statements asked. Given: ∠BTO ≅ ∠IWE WI ≅ BT , OW ≅ ET Prove: △
Varvara68 [4.7K]

Answer:

\triangle BOT \cong \triangle IEW

Step-by-step explanation:

We are given the following in the question:

\angle BTO \cong \angle IWE\\WI \cong BT\\OT \cong EW

We have to prove:

\triangle BOT \cong \triangle IEW

Proof:

\text{In }\triangle BOT \text{ and } \triangle IEW

we can write:

\angle BTO = \angle IWE\text{ (Given)}\\WI \cong BT\text{ (Given)}\\OT \cong EW\text{ (Given)}

Hence, the two triangle are congruent by SAS congruency rule.

\triangle BOT \cong \triangle IEW

The attached image shows the two triangle.

8 0
3 years ago
Other questions:
  • He hypotenuse of a right triangle is three times the length of one of the legs. the length of the other leg is 648‾‾‾‾√648 feet.
    12·1 answer
  • A hose fills a tank at a rate of 20 gallons per minute.
    9·2 answers
  • How to simplify 81 1/2
    11·2 answers
  • Determine the scale factor of the following dilation. Type a numerical answer in the space provided. Do not type spaces in your
    10·2 answers
  • Find the absolute value of 1 and - 1
    15·2 answers
  • A blood bank needs 9 people to help with a blood drive. 12 people have volunteered. Find how many different groups of 9 can be f
    6·1 answer
  • HELP ASAP WILL MARK BRAINLIEST
    13·1 answer
  • -5/7 divided by -1/3
    12·1 answer
  • The ratio of quarters to dimes in a coin collection is 5 : 3. You add the same number of new quarters as dimes to the collection
    11·2 answers
  • Convert 54.6% to a fraction in simplest form and a decimal.
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!