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
nydimaria [60]
3 years ago
9

Suppose we have a population whose proportion of items with the desired attribute is p = 0:5. (a) If a sample of size 200 is tak

en, find the probability that the proportion of successes in the sample will be between 0.47 and 0.51. Draw a sketch to help you solve this problem and use proper probability notation. (b) If a sample of size 100 is taken, find the probability that the proportion of successes in the sample will be between 0.47 and 0.51. Draw a sketch to help you solve this problem and use proper probability notation.
Mathematics
1 answer:
crimeas [40]3 years ago
8 0

Answer:

a. If a sample of size 200 is taken, the probability that the proportion of successes in the sample will be between 0.47 and 0.51 is 41.26%.

b. If a sample of size 100 is taken, the probability that the proportion of successes in the sample will be between 0.47 and 0.51 is 30.5%.

Step-by-step explanation:

This problem should be solved with a binomial distribution sample, but as the size of the sample is large, it can be approximated to a normal distribution.

The parameters for the normal distribution will be

\mu=p=0.5\\\\\sigma=\sqrt{p(1-p)/n} =\sqrt{0.5*0.5/200}= 0.0353

We can calculate the z values for x1=0.47 and x2=0.51:

z_1=\frac{x_1-\mu}{\sigma}=\frac{0.47-0.5}{0.0353}=-0.85\\\\z_2=\frac{x_2-\mu}{\sigma}=\frac{0.51-0.5}{0.0353}=0.28

We can now calculate the probabilities:

P(0.47

If a sample of size 200 is taken, the probability that the proportion of successes in the sample will be between 0.47 and 0.51 is 41.26%.

b) If the sample size change, the standard deviation of the normal distribution changes:

\mu=p=0.5\\\\\sigma=\sqrt{p(1-p)/n} =\sqrt{0.5*0.5/100}= 0.05

We can calculate the z values for x1=0.47 and x2=0.51:

z_1=\frac{x_1-\mu}{\sigma}=\frac{0.47-0.5}{0.05}=-0.6\\\\z_2=\frac{x_2-\mu}{\sigma}=\frac{0.51-0.5}{0.05}=0.2

We can now calculate the probabilities:

P(0.47

If a sample of size 100 is taken, the probability that the proportion of successes in the sample will be between 0.47 and 0.51 is 30.5%.

You might be interested in
Answer -3(9+3)*2/2*2-(-2)
daser333 [38]

Answer:

-70

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
How to simplifying linear expression
snow_lady [41]
To Simplify It Put It In Y=MX+B Form .
5 0
3 years ago
A local petting zoo had a total of 98,464 visitors last year. The zoo was open every day except thanksgiving, Christmas, and New
riadik2000 [5.3K]

Answer:

The average number of visitors per day is 272.

Step-by-step explanation:

Total number of visitors in the zoo in a year =  98,464

Now,we know that  1 YEAR = 365 DAYS

Also, the zoo was closed on thanksgiving, Christmas, and New Year's Eve

So, the Number of days zoo was open = Total Days in  year -  3 days

= 365 - 3 = 362 days

⇒Number of visitors in  362 days =  98,464

So, \textrm{Number of visitor per day} =  \frac{\textrm{Total number of visitors in 352 days}}{\textrm{352 days}}

= \frac{98,464}{362}  = 272

or, the number of people visiting per day is 272.

Hence,  the average number of visitors per day is 272.

8 0
2 years ago
If gasoline costs $1.99 per gallon and your car gets 27 miles per gallon what is your fuel cost if you travel 600 miles
mezya [45]

600 miles / 27 miles per gallon = 22.22 gallons

22.22 * 1.99 = $44.22 total cost

5 0
3 years ago
Read 2 more answers
A number decreased by fifteen is less than two.
Aliun [14]

Let us assume number of n.

The number is decreased by 15.

Decreasing by 15 means, we need to subtract 15 from that number.

So, it would be come n-15.

Now, it is said that the number would become less than 2.

So, we need to setup an inequality:

n-15 is less than 2.

<h3>n-15 < 2  : required inequality .</h3>

Adding 15 on both sides, we get

n-15+15 < 2+15

n < 17.

<h3>So, we could say the number would be less than 17.</h3>
3 0
3 years ago
Other questions:
  • A car insurance company would like to determine the proportion of accident claims covered by the company. According to a prelimi
    7·1 answer
  • Graph: 20x + 3.00y is greater than or equal to 500
    14·1 answer
  • PLEASE ANSWER ASAP
    15·1 answer
  • Any suggestions or answers
    6·1 answer
  • Carrie and brent leave home at the same time. carrie drives due east at a rate of 30 mph, while brent drives due south at a rate
    13·2 answers
  • Solve the equation for y. 6x+y=12
    10·1 answer
  • When a figure is translated on the coordinate plane you should add or subtract x and y? Is this statement true or false?
    9·1 answer
  • Can someone please help&lt;3
    10·2 answers
  • PLEASE ANSWER QUICKLY! WILL GIVE BRAINIEST! ONE QUESTION! ANSWER CORRECTLY TYSM! &lt;333
    12·1 answer
  • Cindy has $25 saved and earns $12 per week for walking dogs. Mindy has $55 saved and earns $7 per week for watering plants. Cind
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!