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
Basile [38]
3 years ago
13

Suppose a simple random sample of size nequals1000 is obtained from a population whose size is Nequals1 comma 000 comma 000 and

whose population proportion with a specified characteristic is p equals 0.74 . Complete parts​ (a) through​ (c) below. ​(a) Describe the sampling distribution of ModifyingAbove p with caret. A. Approximately​ normal, mu Subscript ModifyingAbove p with caretequals0.74 and sigma Subscript ModifyingAbove p with caretalmost equals0.0139 B. Approximately​ normal, mu Subscript ModifyingAbove p with caretequals0.74 and sigma Subscript ModifyingAbove p with caretalmost equals0.0004 C. Approximately​ normal, mu Subscript ModifyingAbove p with caretequals0.74 and sigma Subscript ModifyingAbove p with caretalmost equals0.0002 ​(b) What is the probability of obtaining xequals770 or more individuals with the​ characteristic? ​P(xgreater than or equals770​)equals nothing ​(Round to four decimal places as​ needed.) ​(c) What is the probability of obtaining xequals720 or fewer individuals with the​ characteristic? ​P(xless than or equals720​)equals nothing ​(Round to four decimal places as​ needed.)
Mathematics
1 answer:
ivanzaharov [21]3 years ago
5 0

Answer:

(a) Correct option is (A).

(b) The value of P (X ≥ 770) is 0.0143.

(c) The value of P (X ≤ 720) is 0.0708.

Step-by-step explanation:

Let <em>X</em> = number of elements with a particular characteristic.

The variable <em>p</em> is defined as the population proportion of elements with the particular characteristic.

The value of <em>p</em> is:

<em>p</em> = 0.74.

A sample of size, <em>n</em> = 1000 is selected from a population with this characteristic.

(a)

According to the Central limit theorem, if from an unknown population large samples of sizes <em>n</em> > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.

The mean of this sampling distribution of sample proportion is:

 \mu_{\hat p}=p

The standard deviation of this sampling distribution of sample proportion is:

 \sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}

The sample selected is of size, <em>n</em> = 1000 > 30.

Thus, according to the central limit theorem the distribution of \hat p is Normal, i.e. \hat p\sim N(\mu_{\hat p}=0.74,\ \sigma_{\hat p}=0.0139).

Thus the correct option is (A).

(b)

We need to compute the value of P (X ≥ 770).

Apply continuity correction:

P (X ≥ 770) = P (X > 770 + 0.50)

                  = P (X > 770.50)

Then \hat p> \frac{770.5}{1000}=0.7705

Compute the value of P(\hat p> 0.7705) as follows:

P(\hat p> 0.7705)=P(\frac{\hat p-\mu_{\hat p}}{\sigma_{\hat p}}>\frac{0.7705-0.74}{0.0139})

                      =P(Z>2.19)\\=1-P(Z

Thus, the value of P (X ≥ 770) is 0.0143.

(c)

We need to compute the value of P (X ≤ 720).

Apply continuity correction:

P (X ≤ 720) = P (X < 720 - 0.50)

                  = P (X < 719.50)

Then \hat p

Compute the value of P(\hat p as follows:

P(\hat p

                      =P(Z

Thus, the value of P (X ≤ 720) is 0.0708.

You might be interested in
Of the ice cream cones sold yesterday at brendan's ice cream shop, 2/5 were chocolate and another 1/2 were vanilla. what fractio
omeli [17]
2/5 + 1/2 = 9/10


2/5 x 2/2 = 4/10
1/2 x 5/5 = 5/10

4/10 + 5/10 = 9/10


9/10 of the ice cream cones sold were either chocolate or vanilla.
7 0
3 years ago
=. What does the expression (x+3)(9) represent? Why?
tresset_1 [31]
Because when you multiply the 9 by x you get 9x and when you multiply the 9 by 3 you get 27. So then your final answer would be 9x + 27.
I hope this helps!! :)

6 0
1 year ago
Number 37, please I need help.
ValentinkaMS [17]
Add all the integers together and then divide by 10 because that’s how many numbers you’re adding.
5 0
3 years ago
Read 2 more answers
The area of triangle is 48 cm sq,its base is 12 cm. find its altitude​
Mariana [72]

Answer:

its altitude is 8 cm

Step-by-step explanation:

1/2× base ×altitude =48

1/2×12× al =48

6×al =48

al = 8

5 0
2 years ago
Which statement is true?
Aneli [31]
The letter has both reflection and rotation symmetry
6 0
2 years ago
Other questions:
  • A function is a special type of a relationship in mathematics. Provide three examples of a function and three examples of a non-
    9·1 answer
  • 649x53 using standard algorithm
    5·1 answer
  • Sin(25)/ 22 = Sin(B)/40<br><br> What is the measure of angle B?
    6·1 answer
  • The function f(x) is a cubic function and the zeros of f(x) are -3, -2, and 1. The y-intercept of f(x) is -24. Write the equatio
    10·1 answer
  • Please help
    9·1 answer
  • Can someone help me with this?
    6·1 answer
  • How do you write 15/60 as a percent
    5·2 answers
  • F(x)=-∣x∣2-3
    12·1 answer
  • Find the value of x.
    14·2 answers
  • This graph shows how the distance daniel runs depends on the number of track practices he attends
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!