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
valina [46]
3 years ago
13

6.8 Use the Normal approximation. Suppose we toss a fair coin 100 times. Use the Normal approximation to find the probability th

at the sample proportion of heads is (a) between 0.3 and 0.7. (b) between 0.4 and 0.65. Moore, David. Exploring the Practice of Statistics & Student CD (p. 325). W.H. Freeman & Company. Kindle Edition.
Mathematics
1 answer:
Maru [420]3 years ago
6 0

Answer:

(a) The probability that proportion of heads is between 0.30 and 0.70 is 1.

(b) The probability that proportion of heads is between 0.40 and 0.65 is 0.9759.

Step-by-step explanation:

Let <em>X</em> = number of heads.

The probability that a head occurs in a toss of a coin is, <em>p</em> = 0.50.

The coin was tossed <em>n</em> = 100 times.

A random toss's result is independent of the other tosses.

The random variable <em>X</em> follows a Binomial distribution with parameters n = 100 and <em>p</em> = 0.50.

But the sample selected is too large and the probability of success is 0.50.

So a Normal approximation to binomial can be applied to approximate the distribution of \hat p<em> </em>(sample proportion of <em>X</em>) if the following conditions are satisfied:

  1. np ≥ 10
  2. n(1 - p) ≥ 10

Check the conditions as follows:

 np=100\times 0.50=50>10\\n(1-p)=100\times (1-0.50)=50>10

Thus, a Normal approximation to binomial can be applied.

So,  \hat p\sim N(p,\ \frac{p(1-p)}{n})

\mu_{p}=p=0.50\\\sigma_{p}=\sqrt{\frac{p(1-p)}{n}}=0.05

(a)

Compute the probability that proportion of heads is between 0.30 and 0.70 as follows:

P(0.30

                              =P(-4

Thus, the probability that proportion of heads is between 0.30 and 0.70 is 1.

(b)

Compute the probability that proportion of heads is between 0.40 and 0.65 as follows:

P(0.40

                              =P(-2

Thus, the probability that proportion of heads is between 0.40 and 0.65 is 0.9759.

You might be interested in
If f(x) = 2x2 – 2, what is<br> X, what is f(-6)<br> give the right answer for a brilliant!
NARA [144]

Answer:

f(- 6) = 70

Step-by-step explanation:

To evaluate f(- 6) , substitute x = - 6 into f(x)

f(- 6) = 2(- 6)² - 2 = 2(36) - 2 = 72 - 2 = 70

5 0
3 years ago
Helppp plsssss!!! Show your work!!<br><br>Thanks
ZanzabumX [31]

First, determine if the boundary line should be dotted or solid. In this case, it should be dotted because the symbol is less than not less than or equal to. This leaves you with options B or D. Now, to see if it should be shaded up or down, test it by substituting any point, let's say the origin (0,0), to see if that point is a solution to the equation. If it is, you shade that side of the graph, but if it's not, you shade the other side of the graph.

0 is less than (-3/4)(0) + 2

0 is less than 2.

Because 0 is actually less than 2, the statement is correct and you shade below the line

Answer: D

6 0
3 years ago
A rocket was launched from the ground and reached its maximum height of 36 feet at
makkiz [27]

Answer:

3 feet

Step-by-step explanation:

36/12=3

3 0
2 years ago
From which source can investors access accurate information about the market prices and movement of stocks?
Nadusha1986 [10]
A, financial newspapers.
8 0
3 years ago
Read 2 more answers
What is the simplest form of this expression?
Dimas [21]

Answer:

(4-m-1)-5

Remove the bracket

= 4-m-1-5

= -2-m

Hope this helps.

7 0
3 years ago
Other questions:
  • Help me with this thanks
    7·1 answer
  • A standard coffee mug has a capacity of 16 fluid ounces. If Annie needs to fill 26 mugs with coffee, how many total quarts of co
    7·1 answer
  • What is 6,214,797 rounded to the nearest hundred thousand ?
    12·1 answer
  • 80 as the product of its prime factors
    15·1 answer
  • I need help with this question on my homework, please help me.
    11·1 answer
  • Select the correct answer from the drop-down menu.
    11·1 answer
  • Choose the correct graph to fit the equation.
    13·1 answer
  • What two numbers is the square root of 23 between?
    6·1 answer
  • 2. (1 point)
    10·1 answer
  • What is 2/5 of 9?
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!