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
Anvisha [2.4K]
3 years ago
5

A random sample of 10 parking meters in a resort community showed the following incomes for a day. Assume the incomes are normal

ly distributed. (a) Find the 95% confidence interval for the true mean and interpret the result. Round to the nearest cent. (b) Find margin of error. $3.60 $4.50 $2.80 $6.30 $2.60 $5.20 $6.75 $4.25 $8.00 $3.00
Mathematics
1 answer:
GenaCL600 [577]3 years ago
4 0

Answer:

A 95% confidence interval for the true mean is [$3.39, $6.01].

Step-by-step explanation:

We are given that a random sample of 10 parking meters in a resort community showed the following incomes for a day;

Incomes (X): $3.60, $4.50, $2.80, $6.30, $2.60, $5.20, $6.75, $4.25, $8.00, $3.00.

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

                         P.Q.  =  \frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }  ~ t_n_-_1

where, \bar X = sample mean income = \frac{\sum X}{n} = $4.70

            s = sample standard deviation = \sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }  = $1.83

            n = sample of parking meters = 10

            \mu = population mean

<em>Here for constructing a 95% confidence interval we have used a One-sample t-test statistics because we don't know about population standard deviation.</em>

<u>So, 95% confidence interval for the population mean, </u>\mu<u> is ;</u>

P(-2.262 < t_9 < 2.262) = 0.95  {As the critical value of t at 9 degrees of

                                            freedom are -2.262 & 2.262 with P = 2.5%}  

P(-2.262 < \frac{\bar X-\mu}{\frac{s}{\sqrt{n} } } < 2.262) = 0.95

P( -2.262 \times {\frac{s}{\sqrt{n} } } < {\bar X-\mu < 2.262 \times {\frac{s}{\sqrt{n} } } ) = 0.95

P( \bar X-2.262 \times {\frac{s}{\sqrt{n} } } < \mu < \bar X+2.262 \times {\frac{s}{\sqrt{n} } } ) = 0.95

<u>95% confidence interval for</u> \mu = [ \bar X-2.262 \times {\frac{s}{\sqrt{n} } } , \bar X+2.262 \times {\frac{s}{\sqrt{n} } } ]

                                         = [ 4.70-2.262 \times {\frac{1.83}{\sqrt{10} } } , 4.70+ 2.262 \times {\frac{1.83}{\sqrt{10} } } ]

                                         = [$3.39, $6.01]

Therefore, a 95% confidence interval for the true mean is [$3.39, $6.01].

The interpretation of the above result is that we are 95% confident that the true mean will lie between incomes of $3.39 and $6.01.

Also, the margin of error  =  2.262 \times {\frac{s}{\sqrt{n} } }

                                          =  2.262 \times {\frac{1.83}{\sqrt{10} } }  = <u>1.31</u>

You might be interested in
What single transformación maps ABC onto ABC ?
Thepotemich [5.8K]

Answer:

a reflection across y-axis then translation of 1 unit right and 2 units up.

a clockwise rotation of 180° about the origin then a translation of 1 unit right and 3 units up

a reflection across y-axis then translation of 1 unit right and 1 unit down

a reflection across y = x then a positive rotation of 270° about the origin

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
And ice cream factory makes 190 quarts of ice cream in five hours how many quarts could be made in 36 hours what was the rate pe
levacccp [35]

190/5 = 38

So, they can make 38 quarts in an hour.

38 * 36 = 1,368

They can make 1,368 quarts in 36 hours.

3 0
3 years ago
The difference of the degrees of the polynomials p(x) = 3x2y2 + 5xy? - x6 and q(x) = 3x5 - 4x3 + 2 is
svet-max [94.6K]

Answer:

The difference of the degrees of the polynomials p (x) and q (x) is 1.

Step-by-step explanation:

A polynomial function is made up of two or more algebraic terms, such as p (x), p (x, y) or p (x, y, z) and so on.

The polynomial’s degree is the highest exponent or power of the variable in the polynomial function.

The polynomials provided are:

p(x) = 3x^{2}y^{2} + 5xy - x^{6}\\\\q(x) = 3x^{5} - 4x^{3} + 2

The degree of polynomial p (x) is:

\text{deg}\ p (x)=6

The degree of polynomial q (x) is:

\text{deg}\ q (x)=5

The difference of the degrees of the polynomials p (x) and q (x) is:

\text{deg}\ p(x)-\text{deg}\ q(x)=6-5=1

Thus, the difference of the degrees of the polynomials p (x) and q (x) is 1.

6 0
3 years ago
Daniella wrote the equation shown to represent “four less than – 3.7 times a number is –11.9.” 4n – (–3.7) = 11.9 Explain her er
Lapatulllka [165]
Her answer represents "-3.7 less than 4 times a number is 11.9". The correct equation should be -3.7n-4=-11.9.
5 0
3 years ago
Read 2 more answers
Draw the shape described below and find its total surface area.
iogann1982 [59]

Answer:

hope this helps :)

Step-by-step explanation:

8:07

Cylinder volume & surface area (video)

3 0
3 years ago
Other questions:
  • If the volume of a sphere is 36pi cubic units, what is the radius?
    14·2 answers
  • 2(-3n-5)-5(4n-8) Simplify
    14·2 answers
  • What is the surface area?
    7·1 answer
  • Evaluate 3w+(8-v)t if w=4, v=5, and t=2<br><br> Please help!!!!
    11·2 answers
  • Factorise: 2x² -7x -4
    7·2 answers
  • Help! PLEASE!! What is the formula? or the answer?
    8·1 answer
  • What is the probability that the web site has between 3 million and 4 million visitors in a single day? If needed, round your an
    9·1 answer
  • Place the indicated product in the proper location on the grid. (y x - 5)(y x + 5)
    9·1 answer
  • Which of the following is true about a parallelogram?
    9·1 answer
  • One number is four less than a second number. Four times the first is 14 more than 5 times the second. Find the numbers.
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!