Slimpfy 48 show all steps

Assume that the one-way commute time of an UoU student from his house to school is a normally distributed random variable which

Marizza181 [45]

Answer:

$n=(\frac{1.960(10)}{5})^2 =15.36 \approx 16$

So the answer for this case would be n=16 rounded up to the nearest integer

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".

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

$\mu$ population mean (variable of interest)

$\sigma=10$ represent the sample standard deviation

n represent the sample size

ME=5 represent the margin of error

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)

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (2)

And on this case we have that ME =5 and we are interested in order to find the value of n, if we solve n from equation (2) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (3)

The critical value for 95% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.025;0;1)", and we got $z_{\alpha/2}=1.96$ , replacing into formula (3) we got:

$n=(\frac{1.960(10)}{5})^2 =15.36 \approx 16$

So the answer for this case would be n=16 rounded up to the nearest integer

3 0

3 years ago

Plz help......................

Mrrafil [7]

I believe the answer would be D.

Hope this helps!

3 0

3 years ago

Read 2 more answers

Please help me vote you brainlest

KIM [24]

Answer: he amount of fabric needed for Jimmy's costume is not stated, we can only determine the amount needed for Rob's costume, which makes it impossible to compare the amounts needed for both of their costumes. If this omission was an error, then you can find the difference between these amounts if the amount needed for Jimmy's costume is stated explicitly.

Step-by-step explanation: The number of yards of fabric needed for Robs costume is (7/8+1/2+1 3/4)÷2

Assuming 1 3/4 is a mixed fraction.

= (7/8 + 1/2 + 7/4) ÷ 2

= (7 + 4 + 2) ÷ (8 × 2)

= 13/16 yards

Suppose 2 yards of fabric is needed for Jimmy's costume, then comparing with Rob's yards, we see that Jimmy's costume requires (2 - 13/16 = 19/16) more yards than Rob's costume.

4 0

3 years ago

Find the difference between the product of 21.23 and 2.04 and the sum of 1.115, 3.18, 22.0613 and 12.2384

umka2103 [35]

The answer is 19.4047.

To find the answer, follow my instructions:
First, find the difference or subtract 21.23 and 2.04. You'll get 19.19.

Second, find the sum or add the numbers 1.115, 3.18, 22.0613, and 12.2384. Remember that when adding numbers that are decimals, you have to align all of the decimal points to get the right answer. The sum of all those numbers are 38.5947.

Third, gather your data. So you got the numbers 19.19, and 38.5947. The question is asking for the difference between them. Remember that difference means subtraction or subtracting/minus. So subtract those numbers. You'll get 19.4047.

I hope you find this answer the most helpful! :)

3 0

3 years ago

an open box is to be made from a piece of metal 16 by 30 inches by cutting out squares of equal size from the corners and bendin

blagie [28]

Let the lengths of the bottom of the box be x and y, and let the length of the squares being cu be z, then
V = xyz . . . (1)
2z + x = 16 => x = 16 - 2z . . . (2)
2z + y = 30 => y = 30 - 2z . . . (3)

Putting (2) and (3) into (1) gives:
V = (16 - 2z)(30 - 2z)z = z(480 - 32z - 60z + 4z^2) = z(480 - 92z + 4z^2) = 480z - 92z^2 + 4z^3
For maximum volume, dV/dz = 0
dV/dz = 480 - 184z + 12z^2 = 0
3z^2 - 46z + 120 = 0
z = 3 1/3 inches

Therefore, for maximum volume, a square of length 3 1/3 (3.33) inches should be cut out from each corner of the cardboard.
The maximum volume is 725 25/27 (725.9) cubic inches.

8 0

3 years ago