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
Semenov [28]
3 years ago
14

A telephone exchange operator assumes that 8% of the phone calls are wrong numbers. If the operator is right, what is the probab

ility that the proportion of wrong numbers in a sample of 421 phone calls would differ from the population proportion by greater than 3%? Round your answer to four decimal places.
Mathematics
1 answer:
Vera_Pavlovna [14]3 years ago
7 0

Answer:

The probability that the sample proportion differ from the population proportion by greater than 3% is 0.0241.

Step-by-step explanation:

Let <em>X</em> = number of phone calls that are wrong numbers.

The proportion of phone calls that are wrong numbers is, <em>p</em> = 0.08.

A sample of<em> </em><em>n</em> = 421 phone calls is selected to determine the proportion of wrong numbers in this sample.

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

The probability mass function of a Binomial distribution is:

P(X=x)={421\choose x}0.08^{x}(1-0.08)^{421-x}

Now, for the sample proportion to differ from the population proportion by 3% the value of the sample proportion should be:

\hat p-p=0.03\\\hat p-0.08=0.03\\\hat p=0.11                            \hat p-p=-0.03\\\hat p-0.08=-0.03\\\hat p=0.05

So when the sample proportion is less than 5% or greater than 11% the difference between the sample proportion and population proportion will be greater than 3%.

  • If sample proportion is 5% then the value of <em>X</em> is,

        X=np=421\times 0.05=21.05\approx21

        Compute the value of P (X ≤ 21) as follows:

       P(X\leq 21)=\sum\limits^{21}_{x=0}{{421\choose x}0.08^{x}(1-0.08)^{421-x}}=0.0106

  • If the sample proportion is 11% then the value of <em>X</em> is,

        X=np=421\times 0.11=46.31\approx47

        Compute the value of P (X ≥ 47) as follows:

       P(X\geq 47)=\sum\limits^{471}_{x=47}{{421\choose x}0.08^{x}(1-0.08)^{421-x}}=0.0135

Then the probability that the sample proportion differ from the population proportion by greater than 3% is:

P(\hat p-p>0.03)=P(X\leq 21)+P(X\geq 47)=0.0106+0.0135=0.0241

Thus, the probability that the sample proportion differ from the population proportion by greater than 3% is 0.0241.

You might be interested in
Another easy question for Branilist.........
OLEGan [10]

Answer:

-4.5

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Consider a graph of the equation y = x + 6. What is the y-intercept?
Ratling [72]
In y = mx + b form, which is what ur equation is in, the y int can be found in the b position

y = mx + b
y = x + 6

as u can see, the number in the b position, ur y int, is 6 <==
7 0
3 years ago
2. 10x - 11 - 4x = 43
Nezavi [6.7K]

Answer:

x=9

Step-by-step explanation:

10x - 11 -4x = 43

6x -11 =43

6x = 54

x=9

8 0
4 years ago
"Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the given st
11111nata11111 [884]

Answer:

The error E = ± 4.04 %

Step-by-step explanation:

Solution:-

- The sample data is used to estimate the population proportion ( p ).

- The success p^ = success percentage = 40 %

- The confidence interval CI = 98%

- The sample size n = 800

- The margin of error E:

- The margin of error "E" for estimation of population proportion ( p ) is given by:

                          E = z-critical*\sqrt{\frac{p~ ( 1 - p~ )}{n} }

Where, Z-critical value is defined by the significance level:

                         P ( Z < Z-critical ) = α / 2

Where, α : Significance level

                          α = 1 - CI

                         P ( Z < Z-critical ) = (1 - 0.98) / 2

                         P ( Z < Z-critical ) = 0.01  

                         Z-critical = 2.33

- The error E of estimation is:

                        E = 2.33*\sqrt{\frac{0.4 ( 1 - 0.4 )}{800} }\\\\E = 0.04035

- The error E = ± 4.04 %

6 0
3 years ago
A soccer ball on the ground is kicked with an initial velocity of 37 feet per second at an elevation angle of 70°. Which
Montano1993 [528]

Answer:

x(t) = 37cos(70o)t and y(t) = –16t2 + 37sin(70o)t

Step-by-step explanation:

6 0
3 years ago
Other questions:
  • The function f(x) = –x2 − 2x + 15 is shown on the graph. What are the domain and range of the function?
    12·1 answer
  • 21 is less than a number
    9·1 answer
  • A scientist is working with two different concentrations of hydrochloric acid (HCl) . One bottle is 70% HCl, and the other is 30
    10·1 answer
  • URGENT EXPLANATION Solve the Inequality
    14·1 answer
  • Martin kept track of the number of times he had to flip a coin before it landed tails up.
    8·2 answers
  • I need help with this plssss<br> Expert plsss help meeeee
    7·2 answers
  • A formula for finding SA, the surface area of a rectangular prism, is
    9·1 answer
  • I need this for homework plz help me.
    12·2 answers
  • Enter the missing exponent.<br> 9/49 = ( 3/7 )^
    14·1 answer
  • Solve the inequality and the graph the solution
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!