A used car dealership surveyed 50 customers who bought a card from them two years ago. 78% of customers said that they would recommend this dealership to their friends. What is the 90% confidence interval for the percent of all former buyers who would recommend this dealership to their friends

Answer:

The 90% confidence interval for the percent of all former buyers who would recommend this dealership to their friends is (68.36%, 87.64%).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

A used car dealership surveyed 50 customers who bought a card from them two years ago. 78% of customers said that they would recommend this dealership to their friends.

This means that [tex]n = 50, \pi = 0.78[/tex].

90% confidence level

So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.78 - 1.645\sqrt{\frac{0.78*0.22}{50}} = 0.6836[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.78 + 1.645\sqrt{\frac{0.78*0.22}{50}} = 0.8764[/tex]

As a percent:

0.6836*100% = 68.36%

0.8764*100% = 87.64%

The 90% confidence interval for the percent of all former buyers who would recommend this dealership to their friends is (68.36%, 87.64%).

What is the volume of a cube with a side length that measures 1 1/2 ft? Enter your answer in the box.

which is correct?????

help me plzz
4X + 24 - X + 5 ≤ 62

Evaluate using suitable property. Write the needed steps. Use proper brackets.
20 x 399 x 5

Please help me solve these questions

9. Find the measure of angle
a
36°
57°

The area of the shape is [ ]
square meters.
(50 points ^^)

pls help thannnnkkkss <33

A developer is building a scale model of the city. From the roof of an apartment complex, the developer points two lasers at the taller office building across the street. The first laser points to the base of the building and the second laser points to the top of the building. The first laser beam has an angle of depression of 36° and is 155.7 feet long. The second has an angle of elevation of 32° and is 148.6 feet long. How tall is the office building? How far apart are the apartment complex and the office building? Round your answers to the nearest foot.

Laura is bowling 5 games. Her first 4 scores were 103, 143, 101, and 110.
To end up with an average score of at least 126.8, what is the lowest score Laura will need in the fifth
game?

Mi mamá Rosa Amelia, asistió al Hospital cercano a su casa, luego de hacer atendida, el medico tratante le dio tres tipos de pastillas que tomar;la pastilla rojas cada 12 horas, la pastilla amarilla 8 horas y la pastilla blanca cada 7 horas. Si empieza a tomarse la pastilla en el día de hoy a las 12:00 del mediodía Cuándo volverá a tomarse cada pastilla otra vez?​

HELP, ASAPPP, Unit 1: Performing Transformations

A young entrepreneur wants to set up a lemonade stand at a busy intersection. Customers arrive at a rate of 38 customers per hour according to a Poisson distribution. Customers will be served at the average rate of 58 customers per hour with exponential service times. What is the average utilization rate (%) of the entrepreneur

What do patterns do you notice about finding the area of a triangle?

HELLLP PLZZZZ , i need to anwer this quastion is a major grade :((

IF YOU AWNSER THIS ILL GIVE U 5$

410 people were surveyed about their favorite color. The circle graph created from the results shows that the slice for red measures 130 degrees. How many people said their favorite color was red?

1. Which of the following equations would not
contain the point (4, 12)?

A.y = 2X + 9

B.y = -2x + 14-x1

C. y = 2x + 8

D. y = -2x + 20

Each square represents 1 whole. Which of the following are represented by the model shown? Select the three correct answers.

Give the most precise selection
for the quadrilateral with the
following vertices.
P(0,0), Q(2a, 2b), R(20,2b), S(20,0)

I need help with problem number 3 if someone can help me with that

The winter clothing drive has received donations of 5 coats,23 pairs of gloves, 19 scarves, and 3 hats so far.

PLZ HELP I WILL GIVE BRAINLIEST ANSWER EACH QUESTION PLZ THANKS!!!!!!

HELP !!!!!!!!!!!!!!!!!!!!!!!

Solve for x 8-2x = 5( x4) ​

Please answer the math question about the Pythagorean theorem

**Template**
B. Answer
C. Answer
D. Answer
E. Answer
F. Answer
G. Answer
H. Answer

Solve the question below.
A + C =5
C + D = 4
C - A = 1
What is D + A?

A man earns 15000 in a month. if he spends 20% on food and 10% in his children's education.
a) what is his total expenditure?
b) how much does he save in a month?​

If f(x) = x3 – 2x2, which expression is equivalent to f(i)?
0-2 + 1
O-2-1
O
2 + 1
O 2-1
PLS HELP

please help! i need this in 10 minutes!!