Ursula says the distance between -5.47 and 5.47 on a number line is equal to |-5.47|. explain her error

In an examination of purchasing patterns of shoppers, a sample of 16 shoppers revealed that they spent, on average, $54 per hour

Lesechka [4]

Answer:

$54-1.64\frac{21}{\sqrt{16}}=45.39$

$54 +1.64\frac{21}{\sqrt{16}}=62.61$

So on this case the 90% confidence interval would be given by (45.39;62.61)

Step-by-step explanation:

Previous concepts

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".

$\bar X=54$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma=21$ represent the sample standard deviation

n=16 represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

Since the Confidence is 0.90 or 90%, the value of $\alpha=1-0.9=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.05,0,1)".And we see that $z_{\alpha/2}=1.64$

Now we have everything in order to replace into formula (1):

$54-1.64\frac{21}{\sqrt{16}}=45.39$

$54 +1.64\frac{21}{\sqrt{16}}=62.61$

So on this case the 90% confidence interval would be given by (45.39;62.61)

4 0

3 years ago

Akira and her puppy are both dressing up as superheroes for Halloween this year. Akira needs 1 yard of cloth for her cape. She a

Ahat [919]

The feet of cloth that she should buy for the capes is 4 feet.

<h3>How many feet should she buy?</h3>

The mathematical operations that would be used to determine the answer are addition and multiplication.

Addition is the process of summing two or more numbers together. Multiplication is the process of determining the product of two or more numbers.

The first step is to convert yard to feet

According to the unit of conversion : 1 yard = 3 feet

1 x 3 = 3 feet

The second step is to add the feet needed for Akira's cape with the foot needed for the puppy's cape

Total feet needed = 3 + 1 = 4 feet

To learn more about addition, please check: brainly.com/question/349488

#SPJ1

8 0

1 year ago

Kaya's family spends $105 to rent a boat for 7 days. The total cost, c, of the boat rental is proportional to the number of days

Elza [17]

Answer:

$c=15d$

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $k=\frac{y}{x}$ or $y=kx$

Let

c ----> the total cost of the boat rental

d ---> is the number of days, the family rents the boat

we know that

Kaya's family spends $105 to rent a boat for 7 days

so

For d=7 days, c=$105

Find the value of the constant of proportionality k

$k=\frac{c}{d}$

substitute the given values

$k=\frac{105}{7}=\$15\ per\ day$

therefore

The linear direct equation is equal to

$c=15d$

8 0

3 years ago

Find the rate of change of the linear function shown in the graph. Then find the initial value.

pantera1 [17]

Answer

ok

Step-by-step explanation

ok

6 0

2 years ago

Use the functions f(x) = 4x − 5 and g(x) = 3x + 9 to complete the function operations listed below.

JulijaS [17]

A:

(f+g)(x)=f(x)+g(x)

(f+g)(x)=4x-5+3x+9

(f+g)(x)=7x+4

B:

(f•g)(x)=f(x)•g(x)

(f•g)(x)=(4x-5)(3x+9)

(f•g)(x)=12x^2-15x+36x-45

(f•g)(x)=12x^2+21x-45

C:

(f○g)(x)=f(g(x))

(f○g)(x)=4(3x+9)-5

(f○g)(x)=12x+36-5

(f○g)(x)=12x+31

6 0

2 years ago