Please help Evaluate 5 - (3/2) to the 3 power A.) 13/8 B.) 9.5 C.) 18.5 D.) 2197/8

The results of a national survey showed that on average, adults sleep 6.3 hours per night. Suppose that the standard deviation i

alekssr [168]

Answer:

a) 75%.

b) 84%

c) Within 2 standard deviations from the mean is 95%. The normal distribution has a higher percentage of observations closer to the mean than a non normal distribution, so this percentage is larger.

Step-by-step explanation:

Empirical Rule:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

Chebyshev Theorem:

The Chebyshev Theorem can also be applied to non-normal distribution. It states that:

At least 75% of the measures are within 2 standard deviations of the mean.

At least 89% of the measures are within 3 standard deviations of the mean.

An in general terms, the percentage of measures within k standard deviations of the mean is given by $100(1 - \frac{1}{k^{2}})$ .

In this question:

Mean: 6.3 hours

Standard deviation: 1.6 hours

(a) Use Chebyshev's theorem to calculate the minimum percentage of individuals who sleep between 3.1 and 9.5 hours.

3.1 = 6.3 - 2*1.6

9.5 = 6.3 + 2*1.6

Within 2 standard deviations, so the minimum percentage is 75%.

(b) Use Chebyshev's theorem to calculate the minimum percentage of individuals who sleep between 2.3 and 10.3 hours.

How many standard deviations from the mean?

One standard deviation is 1.6

These measures are 10.3 = 6.3 = 6.3 - 2.3 = 4. This is k standard deviations, in which

$k = \frac{4}{1.6} = 2.5$

The minimum percentage is:

$100(1 - \frac{1}{k^{2}}) - 100(1 - \frac{1}{2.5^{2}}) = 84%$

So 84%.

(c) Assume that the number of hours of sleep follows a bell-shaped distribution. Use the empirical rule to calculate the percentage of individuals who sleep between 3.1 and 9.5 hours per day.

Within 2 standard deviations from the mean is 95%. The normal distribution has a higher percentage of observations closer to the mean than a non normal distribution, so this percentage is larger.

8 0

3 years ago

Births are approximately Uniformly distributed between the 52 weeks of the year. They can be said to follow a Uniform distributi

Kaylis [27]

Answer:

a) 27

b) 15

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The mean of the uniform distribution is:

$M = \frac{a + b}{2}$

The variance of the uniform distribution is given by:

$V = \frac{(b-a)^{2}}{12}$

The standard deviation is the square root of the variance.

They can be said to follow a Uniform distribution from 1 to 53

This means that $a = 1, b = 53$

a. The mean of this distribution is

$M = \frac{a + b}{2} = \frac{1 + 53}{2} = 27$

b. The standard deviation is:

$s = \sqrt{V} = \sqrt{\frac{(b-a)^{2}}{12}} = \sqrt{\frac{(53-1)^{2}}{12}} = 15$

7 0

4 years ago

PLEASE HELP! WILL UPVOTE!

hram777 [196]

Standard form is
ax+by=c
where a and b and c are integers
and a is normally positivie

y+1/5=3x
minus 3x both sides
-3x+y+1/5=0
minus 1/5 both sides
-3x+y=-1/5
times -5 both sides
15x-5y=1
not listed

8 0

4 years ago

1 Factor completely.

bulgar [2K]

1 Factor completely.

p2+7p+10 = (p + 5)(p + 2)

2 Factor completely.

x2+10x+16 = (x + 4)(x + 6)

3 Factor completely.

x2+7x−18 = (x + 9)(x - 2)

4 Factor completely.

x2−5x−24 = (x - 8)(x + 3)

5 Factor completely.

x2−3x−40 = (x - 8)(x + 5)

6 0

3 years ago

Read 2 more answers

A large university accepts 60% of the students who apply. Of the students the university accepts, 50% actually enroll. If 10,

prisoha [69]

we need to find 1% of 10000 first

so we divide 10000:100= 100 (that's 1%)

to find the 60% which will be accepted we multiply 100 × 60 = 6000 students accepted

of those 6000 we need to find 50% which is ½ so we basically just divide by 2, aka 6000 : 2 = 3000 people which will be enrolled

3 0

3 years ago