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
Advocard [28]
3 years ago
9

A grower believes that one in five of his citrus trees are infected with the citrus red mite. How large a sample should be taken

if the grower wishes to estimate the proportion of his trees that are infected with citrus red mite to within 0.01 with probability 0.95? (Round your answer up to the nearest whole number.)
Mathematics
1 answer:
mihalych1998 [28]3 years ago
5 0

Answer:

n=6147

Step-by-step explanation:

1) Notation and definitions

X=1 number of citrus trees that are infected with the citrus red mite.

n=5 random sample taken

\hat p=\frac{1}{5}=0.2 estimated proportion of citrus trees that are infected with the citrus red mite.

p true population proportion of citrus trees that are infected with the citrus red mite.

Me=0.01 represent the margin of error desired

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

The population proportion have the following distribution

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

In order to find the critical values we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by \alpha=1-0.95=0.05 and \alpha/2 =0.025. And the critical values would be given by:

t_{\alpha/2}=-1.96, t_{1-\alpha/2}=1.96

The margin of error for the proportion interval is given by this formula:  

ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}    (a)  

And on this case we have that ME =\pm 0.01 and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}   (b)  

And replacing into equation (b) the values from part a we got:

n=\frac{0.2(1-0.2)}{(\frac{0.01}{1.96})^2}=6146.56  

And rounded up we have that n=6147

You might be interested in
he Carson family will purchase three used cars. There are two models of cars available, Model A and Model B, each of which is av
beks73 [17]

Answer:

Total number of combination = 32

Step-by-step explanation:

Given:

Number of cars = 3

Number of models = 2.

Number of color = 4

Find:

Total number of combination

Computation:

Total number of combination = [2³ x (2x3) x 4] / !3

Total number of combination = 32

7 0
3 years ago
The 7th graders at Sunview Middle School were helping to renovate a playground for the kindergartners at a nearby elementary sch
Alexus [3.1K]
Please please thank you lord lord thank you please
3 0
3 years ago
Curtis plays a trivia game he earns 2 points for each correct answer and loses 0.25 points for each incorrect answer he get 21 c
Maslowich

Answer:

41

Step-by-step explanation:

Curtis is playing a trivia game.

Number of points earned for each correct answer = 2

Number of points lost for each correct answer = 0.25

Given that:

Number of correct answers given by Curtis = 21

Number of wrong answers given by Curtis = 4

To find:

Total score of the game by Curtis?

Solution:

First of all, let us find the points earned by correct answers.

Points earned by correct answers = Number of correct answers multiplied by Points earned on one correct answer.

Points earned by correct answers = 21 \times 2 = 42

Now, let us find the points to be lost by wrong answers.

Points lost by wrong answers = Number of wrong answers multiplied by Points lost on one correct answer.

Points lost by wrong answers = 4 \times 0.25 = 1

The score of the game can be calculated by subtracting the points lost from the points earned.

Score = 42 - 1 = <em>41</em>

3 0
3 years ago
Solve this equation: 3x-1/5-2/9x=124/5
Vaselesa [24]
Well, you can only combine the numbers with the variable (the x) in front of them, since there’s no other number on the left side of the equation to combine that lone number with

(example: 3x+2+5x; you can only add 3x and 5x together since 2 has no x).

So 3x and -2/9x would be your answer.
6 0
3 years ago
Given cot A = 5/6 and that angle A is in Quadrant I, find the exact value of csc A in
Lerok [7]

Answer: well search It up 1/10

Step-by-step explanation:

8 0
3 years ago
Other questions:
  • In a right triangle, the length of the hypotenuse is 20 inches and the length of one leg is 15 inches. What is the length of the
    6·1 answer
  • Peter is making an "X marks the spot" flag for a treasure hunt. The flag is made of a square white flag with sides of 12 inches.
    14·1 answer
  • Can someone pleaseeeee help me
    9·1 answer
  • A rectangle is drawn on a coordinate plane. Three vertices of the rectangle are points L(−3,10) , M(6,10) , and P(−3,−6) . Point
    6·2 answers
  • Harry’s team has won 13 less than 6 times as many games as it has lost. The team lost n games. Which expression could you use to
    5·1 answer
  • Which two events have the same probability the spinner is divided into 8 equal sections
    14·1 answer
  • Hi I also need help with this please and thank you
    5·1 answer
  • Select the statements which could describe the graph of a non proportional relationship.
    8·1 answer
  • 62% of owned dogs in the United States are spayed or neutered. Round your answers to four decimal places. If 48 owned dogs are r
    13·1 answer
  • Solve for x.<br><br> x / 4 ≥ - 8
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!