What is the value of z in the question sin(4z) = cos(30 + 2z)?

The percentage of body fat of a random sample of 36 men aged 20 to 29 found a sample mean of 14.42. Find a 95% confidence interv

Rina8888 [55]

Answer:

$14.42-1.96\frac{6.95}{\sqrt{36}}=12.150$

$14.42+ 1.96\frac{6.95}{\sqrt{36}}=16.690$

So on this case the 95% confidence interval would be given by (12.150;16.690)

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".

$\bar X=14.42$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma=6.95$ represent the population standard deviation

n=36 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 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that $z_{\alpha/2}=1.96$

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

$14.42-1.96\frac{6.95}{\sqrt{36}}=12.150$

$14.42+ 1.96\frac{6.95}{\sqrt{36}}=16.690$

So on this case the 95% confidence interval would be given by (12.150;16.690)

5 0

3 years ago

You are choosing between two different cell phone plans. The first plan charges a rate of 24 cents per minute. The second plan c

Virty [35]

Answer: 286 minutes

Step-by-step explanation:

x : # of months that has gone by

0.24x : cost of the 24 cent plan after "x" minutes

39.95 + 0.10x : cost of the 10 cent plan after "x" minutes

1. 39.95 + 0.10x > 0.24x

2. 39.95 > 0.24x - 0.10x

3. 39.95 > 0.14x

4. 285.36 > x

x must be AT LEAST 286 minutes for plan #2 (39.95 + 0.10x) to be a better deal

7 0

2 years ago

Read 2 more answers

Round the number 76.4491 to 1 decimal place

solniwko [45]

Answer:

Step-by-step explanation:

76.4

4 0

2 years ago

What type of quadrilateral has to the vertices A(3,6), B(3,3), C(6,3), and D(6,6)

prisoha [69]

a square as the distance between the lengths and widths are 3

8 0

3 years ago

I Need help with 4-7

Murrr4er [49]

Answer:

Step-by-step explanation:

4) parallel because 118° is a supplement to 62° and the corresponding angles are both 118°

5) NOT parallel. The labeled angles sum to 120° and would sum to 180° for parallel lines.

6) NOT parallel. see pic.

If parallel, extending a line to intersect ℓ₁ makes an opposite internal angle which would also be 48°. The created triangle would have its third angle at 180 - 90 - 48 = 42° which is opposite a labeled 48° angle, which is false, so the lines cannot be parallel

7)

b = 78° as it corresponds with a labeled angle above it

a = 180 - 78 = 102° as angles along a line from a common vertex sum to 180

f = is an opposite angle to 180 - 78 - 44 = 58° as angles along a line from a common vertex sum to 180

e = 180 - 90 - 64 = 26° as angles along a line from a common vertex sum to 180

c = 58° as it corresponds with f

d = 180 - 58 = 122° as angles along a line from a common vertex sum to 180

4 0

2 years ago