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
steposvetlana [31]
2 years ago
5

Suppose that p is the probability that a randomly selected person is left handed. The value (1-p) is the probability that the pe

rson is not left-handed. In the sample of 100 people, the function V(p)= 1000 p(1-p) represents the variance of the number of left-handed people in a group of 100.
a) What value of p maximizes the variance?
b) What is the maximum variance?
Mathematics
1 answer:
solmaris [256]2 years ago
3 0

Answer:

a) 1/2

b) 250

Step-by-step explanation:

The start of the question doesn't matter entirely, although is interesting to read. What we are trying to do is find the value for p such that 1000p(1-p) is maximized. Once we have that p, we can easily find the answer to part b.

Finding the value that maximizes 1000p(1-p) is the same as finding the value that maximizes p(1-p), just on a smaller scale. So, we really want to maximize p(1-p). To do this, we will do a trick called completing the square.

p(1-p)=p-p^2=-p^2+p=-(p^2-p)=-(p^2-p+1/4)-(-1/4)=-(p-1/2)^2+1/4.

Because there is a negative sign in front of the big squared term, combined with the fact that a square is always positive, means we need to find the value of p such that the inner part of the square term is equal to 0.

p-1/2=0\\p=1/2.

So, the answer to part a is \boxed{1/2}.

We can then plug 1/2 into the equation for p to find the answer to part b.

1000(1/2)(1-1/2)=1000(1/2)(1/2)=1000*1/4=250.

So, the answer to part b is \boxed{250}.

And we're done!

You might be interested in
What is (−3.2)⋅1.7 multipluied
Natalka [10]

Answer:

-5.44

Step-by-step explanation:

multiply add negative sign

6 0
2 years ago
Read 2 more answers
Suppose that in a random selection of 100 colored​ candies, 26​% of them are blue. The candy company claims that the percentage
quester [9]

Answer:  a) -0.2252, b) 0.8219

Step-by-step explanation:

Since we have given that

Sample size n = 100

Probability that candies are blue = p= 0.26

Probability that company claims that it is blue candy = P = 0.27

So, Q = 1-P= 1-0.27 = 0.73

So, Null hypothesis : H_0:p=P

Alternate hypothesis : H_1:p\neq P

So, the test statistic would be

z=\dfrac{p-P}{\sqrt{\dfrac{P.Q}{n}}}\\\\z=\dfrac{0.26-0.27}{\sqrt{\dfrac{0.27\times 0.73}{100}}}\\\\z=-0.2252

Since α = 0.05

So, critical value of z = 1.96

p-value = P(Z>Z(calculated)

Using the excel function , we get that

P(z>0.2252)\\\\=2\times 0.410.911845\\\\=0.8219

Hence, a) -0.2252, b) 0.8219

6 0
2 years ago
Adrian spends $238 on a DVD. If he buys 18 DVD,s approximately how much money will he spend in all?​
bija089 [108]

Answer:

Adrian would spend exactly $4,284.

Step-by-step explanation:

Multiply the cost by the number of products purchased:

$238 x 18 = $4,284

Have a good day :)

7 0
3 years ago
Read 2 more answers
Castel and Kali are selling wrapping paper for a school fundraiser. Customers can buy rolls of plain wrapping paper and rolls of
True [87]

Answer:

Plain is $7 and Holiday is $15

Step-by-step explanation:

Castel: 2p + 5h = 89

Kali: 9p + 10h = 213

Double Castel's: 4p + 10h = 178

Subtract fro Kali's   9p + 10h = 213

                              - 4p + 10h = 178

5p = 35

p = 7  Plain is $7

Substitute 7 into one of the equations and solve for h:

2(7) + 5h = 89

14 + 5h = 89

5h = 75

h = 15  Holiday is $15

6 0
2 years ago
Example 2: Combining Use of the Multiplication and Addition Rules
bulgar [2K]

Answer:

The probability of getting 6's on both cubes is \frac{1}{36}.

The probability that the total score is at least 11 is \frac{1}{12}.

Step-by-step explanation:

Consider the provided information.

A red cube has faces labeled 1 through 6, and a blue cube has faces labeled in the same way.

Part (A) Both cubes show 6’s.

Probability of getting 6 on red cube is \frac{1}{6}

Probability of getting 6 on blue cube is \frac{1}{6}

Thus, the probability of getting 6's on both cubes is:

P(\text{Both 6's})=\frac{1}{6}\times\frac{1}{6}=\frac{1}{36}

Hence, the probability of getting 6's on both cubes is \frac{1}{36}.

Part (B) The total score is at least 11.

The possible number of outcomes in which total score is at least 11 is:

Red shows 6 and Blue shows 5.

Blue shows 6 and Red shows 5.

Blue shows 6 and Red shows 6.

Thus, the probability of total score is at least 11.

P(\text{Total is at least 11})=\frac{1}{6}\times\frac{1}{6}+\frac{1}{6}\times\frac{1}{6}+\frac{1}{6}\times\frac{1}{6}\\P(\text{Total is at least 11})=\frac{1}{12}

Hence, the probability that the total score is at least 11 is \frac{1}{12}.

3 0
3 years ago
Other questions:
  • Brittany is sell car magnets. She purchases them for $7.50 each and marks up the price by 30%. How much is Brittany planning to
    14·2 answers
  • when a decimal is written in word form, what indicates that the equivalent form is a mixed number and not a fraccion? Explain.
    11·1 answer
  • What is the answer for <br>9=81×
    9·2 answers
  • All of the following words mean the same thing as conservation except
    7·2 answers
  • We have two fractions, \dfrac{1}{6} 6 1 ​ start fraction, 1, divided by, 6, end fraction and \dfrac{3}{8} 8 3 ​ start fraction,
    5·1 answer
  • To prepare for wrestling season, Tommy wants to eat 24 grams of protein at breakfast. He knows that there are 3 grams of protein
    11·2 answers
  • Hector drank 6 glasses of orange juice that contained a total of 360 calories. What was the unit rate (calories per glass)?
    15·2 answers
  • Nielsen Rating: The television show nbc Sunday night football broadcast a game between the colts and patriots and received a sha
    12·1 answer
  • Find the magnitude of (3,4,9)
    10·1 answer
  • Using the distributive property and expanded form to solve what is 8(a + 3b)
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!