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
makkiz [27]
3 years ago
10

A town council wants to estimate the proportion of residents who are in favor of a proposal to upgrade the computers in the town

library. A random sample of 100 residents was selected, and 97 of those selected indicated that they were in favor of the proposal. Is it appropriate to assume that the sampling distribution of the sample proportion is approximately normal?
Mathematics
2 answers:
amm18123 years ago
6 0

Answer:

We need to check the conditions in order to use the normal approximation.

1) np=100*0.97=97 > 10

2) n(1-p)=100*(1-0.97)=3 < 10

For this case the first condition is satisfied but the second NO, so then is not appropiate for this case use the normal approximation given by:

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

Step-by-step explanation:

For this case we have the following info given:

n = 100 represent the sample size

x= 97 represent the people selected who  indicates that they were in favor of the proposal

The estimated proportion for this case is given by:

\hat p =\frac{x}{n}= \frac{97}{100}=0.97

We need to check the conditions in order to use the normal approximation.

1) np=100*0.97=97 > 10

2) n(1-p)=100*(1-0.97)=3 < 10

For this case the first condition is satisfied but the second NO, so then is not appropiate for this case use the normal approximation given by:

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

Anika [276]3 years ago
4 0

Answer:

Since n(1-p) < 5, it is not appropriate to assume that the sampling distribution of the sample proportion is approximately normal.

Step-by-step explanation:

Binomial probability distribution:

Probability of x sucesses on n repeated trials, with p probability.

Can be approximated to the normal distribution if:

np > 5 and n(1-p) > 5

In this problem:

A random sample of 100 residents was selected, and 97 of those selected indicated that they were in favor of the proposal.

This means that n = 100, p = \frac{97}{100} = 0.97

Is it appropriate to assume that the sampling distribution of the sample proportion is approximately normal?

np = 100*0.97 = 97 > 5

n(1-p) = 100*0.03 = 3 < 5

Since n(1-p) < 5, it is not appropriate to assume that the sampling distribution of the sample proportion is approximately normal.

You might be interested in
If x + 9.8 = 14.7, what is the value of 8(x - 3.7)?
Scrat [10]
Find the value of x
x+9.8=14.7
x=4.9
Then plug it in the second equation
8(4.9-3.7)
8(1.2)
9.6
Hope this helps.
5 0
3 years ago
Read 2 more answers
(15 points and brainliest) If x = 0 and y &lt; 0, where is the point (x, y) located? A. on the x axis B. on the y axis
nikklg [1K]

Answer:

On the y axis

Step-by-step explanation:

If x is zero, it automatically has to be on the y axis because x=0 is where the x and y axis intersect.

6 0
3 years ago
Si consideras como base uno de los rectángulos de dimensiones de 5cm y 3cm ¿cuanto mide la altura de ese prisma?
Vinvika [58]

Respuesta:

h = V / 15

Explicación paso a paso:

El volumen de un prisma rectangular se calcula usando la relación:

Largo ancho alto

Donde, largo y ancho son la dimensión de la base

Por eso,

Volumen = Base * altura

Volumen = (5 cm * 3 cm) * altura

De la pregunta, no se da el volumen, por lo tanto, tomamos el volumen como V en otro para calcular la altura, h

V = 15h

Divide ambos lados entre 15

V / 15 = 15h / 15

V / 15 = h

5 0
3 years ago
Find x if f(x) = 2x + 7 and f(x) = -1.
damaskus [11]
The answer is positive 5
7 0
3 years ago
Read 2 more answers
You leave a 20% tip on your $70 dinner bill. How much was the tip
jonny [76]

\frac{20}{100}  \times70 =  \frac{1}{5}   \times 70 \\ = 14
hey hope this helps
5 0
3 years ago
Other questions:
  • Your cat is trapped on a tree branch 10 feet above the ground. Your ladder is only 12 feet long. If you place the ladder’s
    7·1 answer
  • Help pls I have no clue
    7·1 answer
  • Whhat's the Answer tho
    13·1 answer
  • HELP ME PLEASE SOMEONE
    9·1 answer
  • How many rational numbers are there between - 5 and - 4?​
    6·1 answer
  • What is the area of this trapezoid?
    8·2 answers
  • Question 1 A) f(x)=2^x and g(x)=3−x I got 3x^2+12 don't know if im right B) i need help for this f(x)=sinx and g(x)=x
    12·1 answer
  • Can someone please work out both problems, I need help with my math hw due in 4 hours
    9·1 answer
  • Algebra 1 Homework Thanks to whoever helps, have a nice day;)
    10·2 answers
  • My school's enrollment is $506$ after a $10\%$ increase. What was the school's enrollment before the increase? 25 POINTS!!!!!!!!
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!