Ask question

Ask question

All categories

murzikaleks [220]

2 years ago

11

The time to complete the construction of a soapbox derby car is normally distributed with a mean of three hours and a standard d

eviation of one hour. Find the probability that it would take exactly 3.7 hours to construct a soapbox derby car

1 answer:

Bezzdna [24]2 years ago

3 0

Answer:

0% probability that it would take exactly 3.7 hours to construct a soapbox derby car

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Also, the probability of finding an exact value in the normal probability distribution is 0.

So

0% probability that it would take exactly 3.7 hours to construct a soapbox derby car

You might be interested in

It is known that driving can be difficult in regions where winter conditions involve snow-covered roads. For cars equipped with

noname [10]

Answer:

The null and alternative hypothesis for this test are

$H_0: \mu\ge 215\\\\H_1: \mu< 215$

Step-by-step explanation:

If we perform a hypothesis test, we can reject or not reject the null hypothesis.

To conclude that the tires have a decreased stopping distance (μ<215), we should state the null hypothesis $H_0: \mu\ge 215$ and then go on with the analysis to reject it (or not).

If the null hypothesis is rejected, the claim of the manufacturer is rigth.

The alternative hypothesis would be $H_1: \mu$ , that would turn rigth if the null hypothesis is rejected.

5 0

2 years ago

Erick, Mia, and Isabelle golfed 9 holes. Erick scored 10 more than Mia, and Isabelle scored 16 less than twice Mia's score. Use

klasskru [66]

X + x + 10 + 2x - 16

x = mia's score
x + 10 = erick's score
2x - 16 = isabelle's score

the entire expression is the sum of all 3 scores <==

3 0

1 year ago

Which situation can be represented by the equation below?<br>15 - x = 63.75

storchak [24]

Answer:

The last one

Step-by-step explanation:

The first one would be multiplication because you want to find the total thickness, the second one is division because it gives the total value and the amount of bags, the third one is addition because it gives you a starting value and says that they work this amount more in this month, and the last one is subtraction because he first pays with a gift card, and then with cash.

Hopefully that helped

4 0

2 years ago

Find the dimensions of the box with volume 1728 cm3 that has minimal surface area. (Let x, y, and z be the dimensions of the box

Gala2k [10]

Answer:

The dimensions of the box are 12 cm , 12 cm , 12 cm

Step-by-step explanation:

Let x , y and z be the dimensions of box

Volume of box =xyz=1728

$z=\frac{1728}{xy}$

Surface area of box = $2xy+2yz+2xz=2xy+2y(\frac{1728}{xy})+2x(\frac{1728}{xy})$

Let $f(x,y)=2xy+2(\frac{1728}{x})+2(\frac{1728}{y})$

To get minimal surface area

$\frac{\partial f}{\partial x}=0$ and $\frac{\partial f}{\partial y}=0$

$\frac{\partial(2xy+2(\frac{1728}{x})+2(\frac{1728}{y}))}{\partial x}=0$

$2y-2(\frac{1728}{x^2})=0$

$y=\frac{1728}{x^2}$ ----1

$\frac{\partial(2xy+2(\frac{1728}{x})+2(\frac{1728}{y}))}{\partial y}=0$

$2x-2(\frac{1728}{y^2})=0\\x=\frac{1728}{y^2} \\y^2=\frac{1728}{x}$

Using 1

$(\frac{1728}{x^2} )^2=\frac{1728}{x}$

x=0 and $x^3=1728$

Side can never be 0

So, $x^3=1728$

x=12

$y=\frac{1728}{x^2} \\y=\frac{1728}{12^2}$

y=12

$z=\frac{1728}{xy}\\z=\frac{1728}{(12)(12)}$

z=12

The dimensions of the box are 12 cm , 12 cm , 12 cm

5 0

2 years ago

The Fortune 500 is comprised of Fortune magazine's annual list of the finite population of the top 500 companies in the U.S. ran

Serjik [45]

Answer:

The standard error of the proportion is 0.0367.

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the standard error is $s = \sqrt{\frac{p(1-p)}{n}}$

In this question:

$p = 0.16, n = 100$

So

$s = \sqrt{\frac{0.16*0.84}{100}} = 0.0367$

The standard error of the proportion is 0.0367.

4 0

1 year ago