Please heelllppppppoo

A recent survey describes the total sleep time per night among college students as approximately Normally distributed with mean

marin [14]

Answer:

a) $\sigma_{\bar X}= \frac{1.26}{\sqrt{165}}= 0.0981$

b) We expect 68% of the values between : (6.6219, 6.8181)

We expect 95% of the values between : (6.5238, 6.9162)

We expect 99.7% of the values between : (6.4257, 7.0143)

c) $z = \frac{6.9-6.72}{0.0981}= 1.835$

And we can use the z normal table or excel and we got:

$P(Z$

Step-by-step explanation:

Previous concepts

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".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Let X the random variable that represent the total sleep time of a population, and for this case we know the distribution for X is given by:

$X \sim N(6.72,1.26)$

Where $\mu=6.72$ and $\sigma=1.26$

(a) What is the standard deviation for the average time in hours? (Round your answer to four decimal places.)

For this case the sample mean have the following distirbution

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

And the deviation is given by:

$\sigma_{\bar X}= \frac{1.26}{\sqrt{165}}= 0.0981$

in minutes?= (Round your answer to three decimal places.)

(b) Use the 95 part of the 68–95–99.7 rule to describe the variability of this sample mean. (Round your answer to four decimal places.)

The empirical rule, also known as three-sigma rule or 68-95-99.7 rule, "is a statistical rule which states that for a normal distribution, almost all data falls within three standard deviations (denoted by σ) of the mean (denoted by µ)".

• The probability of obtain values within one deviation from the mean is 0.68

• The probability of obtain values within two deviation's from the mean is 0.95

• The probability of obtain values within three deviation's from the mean is 0.997

We expect 68% of the values between : (6.6219, 6.8181)

We expect 95% of the values between : (6.5238, 6.9162)

We expect 99.7% of the values between : (6.4257, 7.0143)

(c) What is the probability that your average will be below 6.9 hours? (Round your answer to four decimal places.)

For this case we can use the z score formula given by:

$z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

And we can find the z score for 6.9 and we got:

$z = \frac{6.9-6.72}{0.0981}= 1.835$

And we can use the z normal table or excel and we got:

$P(Z$

4 0

3 years ago

Hey guys ( or gals ) I have no idea what to do please help me.

shepuryov [24]

Answer:

Irrational numbers cannot be written as a fraction, or the ratio of two whole numbers.

You would have to find a GCF (greatest common factor) and multiply it out of the radical.

ex.

$\sqrt{6}$ = 2 x 2 x 2

when you have to multiplier numbers then you can combine two of them to take outside the radical, meaning 2x2x2

2 $\sqrt{2\\}$

so $\sqrt{6}$ would be closest to the positive 2 on the number line and 2 notches.

$\sqrt{11}$

is an irrational number, so it might fall into 3.3 if turned into a decimal.

Step-by-step explanation:

8 0

3 years ago

You have 59 to spend on lip balm and hand sanitizer. The equation 1.5x + 2.5y = 9 represents this situation, where x is tubes of

il63 [147K]

Answer:

Step-by-step explanation:

you have to keep the x and the y sepret and then you can divied one by nine then you get the answer so there you go

3 0

3 years ago

A deck of ordinary cards is shuffled and 13 cards are dealt. What is the probability that the last card dealt is an ace?

alexandr1967 [171]

Answer:

The probability that the last card dealt is an ace is $\frac{1}{13}$ .

Step-by-step explanation:

Given : A deck of ordinary cards is shuffled and 13 cards are dealt.

To find : What is the probability that the last card dealt is an ace?

Solution :

There are total 52 cards.

The total arrangement of cards is 52!.

There is 4 ace cards in total.

Arrangement for containing ace as the 13th card is $4\times 51!$ .

The probability that the last card dealt is an ace is

$P=\frac{4\times 51!}{52!}$

$P=\frac{4\times 51!}{52\times 51!}$

$P=\frac{4}{52}$

$P=\frac{1}{13}$

Therefore, the probability that the last card dealt is an ace is $\frac{1}{13}$ .

4 0

3 years ago

HELP MEE!!!|||||||||Find the volume of a cylinder with a diameter of 6 inches and a height that is three times the radius. Use 3

natulia [17]

Answer: There are several information's of immense importance already given in the question. Let us write them down first.

Diameter of the cylinder = 6 inches

Then

Radius of the cylinder = 3 inches.

Height of the cylinder = 3 * radius

= 3 * 3

= 9 inches

Volume of the cylinder = (pi) * (Radius)^2 * Height

= 3.14 * (3)^2 * 9

= 3.14 * 9 * 9

= 254.34 cubic inches

7 0

3 years ago