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
Which statement is true about figures ABCD and A′B′C′D′? (1 point)
sladkih [1.3K]

Answer:

Step-by-step explanation:

A'B'C'D' is obtained by rotating ABCD 180° counterclockwise about the origin and then reflecting it across the x-axis.

A(2, -2) is mapped to A'(-2, -2)

B(1, -4) is mapped to B'(-1, -4)

C(0, -2) is mapped to C'(0, -2)

D(1, -1) is mapped to D'(-1, -1)

If we rotate counterclockwise 180°, every point (x, y) is mapped to (-x, -y):

A(2, -2) gets mapped to (-2, 2)

B(1, -4) gets mapped to (-1, 4)

C(0, -2) gets mapped to (0, 2)

D(1, -1) gets mapped to (-1, 1)

Reflecting these images across the x-axis will then map (x, y) to (x, -y):

(-2, 2) gets mapped to (-2, -2)

(-1, 4) gets mapped to (-1, -4)

(0, 2) gets mapped to (0, -2)

(-1, 1) gets mapped to (-1, -1)

These new coordinates are the same as A'B'C'D'.

3 0
2 years ago
ladder is 8 ft long . The ladder needs to reach to a window that is 6 ft above the ground . How far away from the house should t
stiks02 [169]

Answer:

5.3 or 28

Step-by-step explanation:

6^{2}+b^{2}=8^{2}

36+b^{2}=64

64-36=28

\sqrt{28\\}

=5.29 or 5.3

5 0
2 years ago
Giving everything. Plzzz help.
jarptica [38.1K]
Pretty sure it’s A sorry if that’s wrong
8 0
3 years ago
Read 2 more answers
The price for certain produce items at Greg's local supermarket are
Vaselesa [24]
72.28 i took the test it was easy bro
8 0
3 years ago
Write an equation for each translation of y = |x|
nata0808 [166]
If you want to write an equation for an absolute value function this is the parent function y=a|x-h|+k.

In order to write an equation that is 16.5 units right you would do this:

y=|x-16.5|
If you are moving units left the number -16.5 would become 16.5

Remember when you are moving that the number inside is always the opposite sign of where you are moving 

Here is the answer:
y=|x-16.5|
Hope This Helps!
3 0
3 years ago
Read 2 more answers
Other questions:
  • Focus groups of 15 people are randomly selected to discuss products of the Yummy Company. It is determined that the mean number
    9·1 answer
  • Can someone please answer this question I will give brainliest for correct answers.
    5·1 answer
  • Hello please help! posted picture of question
    10·1 answer
  • Need help with geometry.
    15·1 answer
  • A cone ___ has a square base<br> never<br> always<br> sometimes
    13·2 answers
  • A rectangular plot of land is represented on a coordinate plane where each unit is one foot. The vertices are at (50,20), (50,90
    6·2 answers
  • Easy car rental charges 8.50$ and hour plus a rental free of 25.50$ write an expression <br>,​
    6·1 answer
  • What is -3/1 2 -2 3.​
    8·1 answer
  • You paint four walls. Each wall is a rectangle with a length of 20 feet and a height of 12 feet. One gallon of paint covers abou
    13·1 answer
  • I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!