Brandon enters bike races. He bikes 9

Here are summary statistics for randomly selected weights of newborn girls: nequals=174174, x overbarxequals=30.930.9 hg, seq

MaRussiya [10]

Answer:

The 95% confidence interval would be given by (29.780;32.020)

Step-by-step explanation:

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".

$\bar X=30.9$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s=7.5 represent the sample standard deviation

n=174 represent the sample size

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

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

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=174-1=173$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-T.INV(0.025,173)".And we see that $t_{\alpha/2}=1.97$ , this value is similar to the obtained with the normal standard distribution since the sample size is large to approximate the t distribution with the normal distribution.

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

$30.9-1.97\frac{7.5}{\sqrt{174}}=29.780$

$30.9+1.97\frac{7.5}{\sqrt{174}}=32.020$

So on this case the 95% confidence interval would be given by (29.780;32.020)

The value 29.6 is not contained on the interval calculated.

5 0

3 years ago

Hey guys what is 10+12-34+68-4778855+5676+77-6865666+3456-7658×45×23+35566÷79997 = ?

elena55 [62]

Answer:

-19561285.5554

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

If a town starts with population of 63,500 that declines by 700 people each year, construct an equation to model its population

ankoles [38]

The equation would be 63500-700x=P, where 63500 is the original population, -700 is the amount the population decreases each year, x is the number of years, and P is the total population.

To answer the second part of the question, plug in 53000 for P and solve for x:

63500-700x=53000

*Subtract 63500 from both sides*

-700x=-10500

*Divide both sides by -700*

x=15

It would take 15 years for the population to drop to 53000.

Hope this helps!!

6 0

2 years ago

A company mixes two kinds of cleansers to get a blend they sell for 59 cents a liter. One of the cleansers costs 50 cents per li

Lilit [14]

Answer:

Cleanser that costs 50 cents is 1400 liters, Cleanser that costs 80 cents is 600 liters.

Step-by-step explanation:

We can solve this by using simultaneous equations:

Let us express the question in terms of equations

Let a be cleanser at 50 cents and let b be the cleanser at 80 cents.

Equation 1: 0.5a + 0.8b = 0.59(a+b)

Equation 2: a + b = 2000

From equation 2, a = 2000 - b (Let's call this equation 3)

2. Substituting equations 2 and 3 in Equation 1:

0.5a + 0.8b = 0.59(a+b)

0.5(2000 - b) + 0.8b = 0.59(2000)

1000 - 0.5b + 0.8b = 1180

0.3b = 180

b = 600

Substitute in equation 3:

a = 2000 - 600

a = 1400

As a note, I formed equation 1 because I know for a fact the cost per liter of a and b. I also know it is sold at 0.59 cents per liter. We are selling 2000 liters in this instance, therefore 0.59(2000) = 1180, which in this case is the selling price.

4 0

3 years ago

Find the surface area of this cube. Be sure to include the correct unit in your answer

alexandr1967 [171]

Answer:

384 inches squared

Step-by-step explanation:

The surface area for one of the sides is 8 x 8 = 64

There are 6 sides so 64 x 6 = 384

4 0

2 years ago