Gregory bought 0.85 pounds of apples, they cost 1.49 a pound. about how much did gregory spend on apples

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

2 years ago

A florist gathered data about the weekly number of flower deliveries he made to homes and to businesses for several weeks. He us

shutvik [7]

Answer:

The number of deliveries that are predicted to be made to homes during a week with 50 deliveries to business is 87 deliveries

Step-by-step explanation:

The data categorization are;

The number of home deliveries = x

The number of delivery to businesses = y

The line of best fit is y = 0.555·x + 1.629

The number of deliveries that would be made to homes when 50 deliveries are made to businesses is found as follows;

We substitute y = 50 in the line of best fit to get;

50 = 0.555·x + 1.629 =

50 - 1.629 = 0.555·x

0.555·x = 48.371

x = 48.371/0.555= 87.155

Therefore, since we are dealing with deliveries, we approximate to the nearest whole number delivery which is 87 deliveries.

4 0

2 years ago

If a lot contains 48,000 square feet and is 240' wide, how deep is the lot?

lisabon 2012 [21]

We would assume the lot takes a rectangular shape. With that in mind. the area of the rectangular plot is 48, 000 and its width is 240. We only need to know the area of a rectangle which is L * W.
So 48, 000 = L * 240
L = 48, 000/ 240
L = 200
It is 200 square feet deep.

6 0

2 years ago

The thickness of a ﬂange on an aircraft component is uniformly distributed between 0.95 and 1.05 millimeters. Determine the foll

Mrrafil [7]

Answer

given,

thickness of a ﬂange on an aircraft component is uniformly distributed between 0.95 and 1.05 millimeters.

X = U[0.95,1.05] 0.95≤ x ≤ 1.05

the cumulative distribution function of flange

F(x) = P{X≤ x}= $\dfrac{x-0.95}{1.05-0.95}$

= $\dfrac{x-0.95}{0.1}$

b) P(X>1.02)= 1 - P(X≤1.02)

= $1- \dfrac{1.02-0.95}{0.1}$

= 0.3

c) The thickness greater than 0.96 exceeded by 90% of the ﬂanges.

d) mean = $\dfrac{0.95+1.05}{2}$

= 1

variance = $\dfrac{(1.05-0.95)^2}{12}$

= 0.000833

4 0

2 years ago

8 times of the eight term of an arithmetic progression is equal to 12 times of the twelfth term. find its first term if the comm

denpristay [2]

Answer:

38

Step-by-step explanation:

We can express the 8th term as x and the 12th term as y.

This would mean that 8x=12y

Because the common difference between terms is -2 and term 8 and term 12 are 4 terms apart, this means that the 12th term is 8 less than the 8th term, so x-8=y

Now we can use this to substitute y with x in the first equation. This would give us:

8x=12(x-8)

Which we can expand and solve:

8x=12x-96

-4x=-96

Therefore x=24

This means the 8th term is 24 and the 12th term is 16 (24-8).

To test if this is correct we can do:

8x24=12x16

Which indeed are equal, both sides multiply to 192.

Now that we have our 8th term, we can find the 1st term, which is 7 terms away, therefore we just add 14 to the 8th term 24. (7x2=14)

24+14=38.

The first term is 38.

Hope this helped!

3 0

2 years ago