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
MissTica
3 years ago
11

A simple random sample of size nequals10 is obtained from a population with muequals68 and sigmaequals15. ​(a) What must be true

regarding the distribution of the population in order to use the normal model to compute probabilities involving the sample​ mean? Assuming that this condition is​ true, describe the sampling distribution of x overbar. ​(b) Assuming the normal model can be​ used, determine ​P(x overbarless than71.4​). ​(c) Assuming the normal model can be​ used, determine ​P(x overbargreater than or equals69.1​).
Mathematics
1 answer:
valentina_108 [34]3 years ago
7 0

Answer:

(a) The distribution of the sample mean (\bar x) is <em>N</em> (68, 4.74²).

(b) The value of P(\bar X is 0.7642.

(c) The value of P(\bar X\geq 69.1) is 0.3670.

Step-by-step explanation:

A random sample of size <em>n</em> = 10 is selected from a population.

Let the population be made up of the random variable <em>X</em>.

The mean and standard deviation of <em>X</em> are:

\mu=68\\\sigma=15

(a)

According to the Central Limit Theorem if we have a population with mean <em>μ</em> and standard deviation <em>σ</em> and we take appropriately huge random samples (<em>n</em> ≥ 30) from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.

Since the sample selected is not large, i.e. <em>n</em> = 10 < 30, for the distribution of the sample mean will be approximately normally distributed, the population from which the sample is selected must be normally distributed.

Then, the mean of the distribution of the sample mean is given by,

\mu_{\bar x}=\mu=68

And the standard deviation of the distribution of the sample mean is given by,

\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{15}{\sqrt{10}}=4.74

Thus, the distribution of the sample mean (\bar x) is <em>N</em> (68, 4.74²).

(b)

Compute the value of P(\bar X as follows:

P(\bar X

                    =P(Z

*Use a <em>z</em>-table for the probability.

Thus, the value of P(\bar X is 0.7642.

(c)

Compute the value of P(\bar X\geq 69.1) as follows:

Apply continuity correction as follows:

P(\bar X\geq 69.1)=P(\bar X> 69.1+0.5)

                    =P(\bar X>69.6)

                    =P(\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}>\frac{69.6-68}{4.74})

                    =P(Z>0.34)\\=1-P(Z

Thus, the value of P(\bar X\geq 69.1) is 0.3670.

You might be interested in
41/50 is closer to 9/11 or 10/11 and explain
Stolb23 [73]
<span>Given number is 41/50,
Now, let’s find which one is closer to the given choices:
=> 9/11
=> 10/11
Notice that the given number and given choices are fraction numbers. In order know which one is closer to the given number, we need to convert these numbers into a decimal.
Note, that in converting a fraction number to a decimal is we need to divide our numerator by our denominator to get the answer.
=> 41/50
=> 0.82
The value of 41/50 is 0.82. Now, let’s find the value of the given choices.
=> 9/11
=> 0.818 or 0.82

=> 10/11
=>0.909 or 0.91

Thus, the correct answer is 9/11 is equals to 41/50.</span>



3 0
3 years ago
For each right triangle below, find the missing side (Pythagorean’s Theorem) and the missing angle (Angle Sum theorem.)
nalin [4]

Answer:     180

i thank hopeful \

6 0
2 years ago
Read 2 more answers
Megan picks a card from a deck of cards numbered 1-10 and rolls a number cube. What is the probability she chooses a card with a
ehidna [41]

Answer:

1/20 if there is only those 10 cards in a deck and 1/26 if there is 52 cards in the deck.

Step-by-step explanation:

There is 3/6 chances to roll a die with an even number, aka 1/2. If there are only 10 cards in the deck and only one of them has the number 5, it's 1/10. To find the probability of both these things happening, multiply the probabilities. 1/10 x 1/2 is equal to 1/20. However, since the question doesn't specify if there is 52 cards like a normal deck and 4 5's etc, there can be a different answer because if there's 52 cards in a deck, 4 of them 5's, the chance of getting a 5 is 4/52 or 1/13 and then you multiply that by 1/2 to get 1/26

4 0
3 years ago
Read 2 more answers
If the length of a rectangle is (x + 7) inches and the width is (3x+2) inches. Which expression represents the rectangle's area?
konstantin123 [22]

Answer:

The answer is no 1:

3x ^{2}  + 23x + 14

5 0
2 years ago
Unit 4 Test, Part 2: Congruence and Constructions<br> Help with my math please
lakkis [162]

Answer/Step-by-sep explanation:

1. Given:

∆NMK ≅ ∆TRP

\overline{NM} = 20

\overline{MK} = 15

\overline{KN} = 25

\overline{TR} = 3x - 1

a. To complete the congruent statement, thus: ∆MNK ≅ ∆RTP

b. The side that is congruent to \overline{TR} is \overline{NM}. Thus:

\overline{TR} ≅ \overline{NM}

c. Since \overline{TR} ≅ \overline{NM}, therefore:

\overline{TR} = \overline{NM}

3x - 1 = 20 (substitution)

Add 1 to both sides

3x = 20 + 1

3x = 21

Divide both sides by 3

x = \frac{21}{3}

x = 7

2. a. Slope of LK = \frac{rise}{run} = \frac{4}{3}

Slope of LM = \frac{rise}{run} = -\frac{3}{5}

b. ✍️Length of LK is the distance between L(-7, 4) and (-4, 8):

Lk = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

Lk = \sqrt{(-4 -(-7))^2 + (8 - 4)^2}

Lk = \sqrt{(3)^2 + (4)^2}

Lk = \sqrt{9 + 16}

Lk = \sqrt{25}

Lk = 5

✍️Length of LM is the distance between L(-7, 4) and (-2, 1):

LM = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

LM = \sqrt{(-2 -(-7))^2 + (1 - 4)^2}

LM = \sqrt{(5)^2 + (-3)^2}

LM = \sqrt{25 + 9}

LM = \sqrt{34}

LM = 5.8 (nearest tenth)

∆KLM is not an isosceles ∆ because it does not has two equal side lengths. This we can see because LK and LM are not equal.

Therefore, Anthony is incorrect. Am isosceles ∆ has two equal sides.

8 0
3 years ago
Other questions:
  • Ndicate in standard form the equation of the line through the given points. P(0, -4), Q(5, 1)
    6·1 answer
  • The algebra teacher said if you square my age then subtract 23 times my age, the result is 50. How old is he?
    12·2 answers
  • Enter the improper fraction as a mixed number 19/6
    5·1 answer
  • How many times does 8 go into 14
    11·2 answers
  • How many cans of food can I buy with $50<br>​
    13·2 answers
  • Complete the equation describing how x and y are related.<br> Please Help Me!!!
    7·2 answers
  • Colby adds 1 and 2 over 3 cups of flour to his mixing bowl and then realizes he put in too much. He take 1 over 4 cup of flour b
    13·1 answer
  • What is 21-123+12*196
    10·1 answer
  • Solve x2 = 144<br> A) x = ±12 <br> B) x = ±72 <br> C) x = ±288 <br> D) x = ±20,736
    10·1 answer
  • If angle A measures 45° 55' 10" and angle B measures 55° 45' 55", then find:​
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!