Find the number of ordered quadruples (a, b, c,

True or false: when comparing two populations, the larger the standard deviation, the more dispersion the distribution has,

Nataliya [291]

<span>It would be...
C) true, because the standard deviation describes how far, on average, each observation is from the typical value. a larger standard deviation means that observations are more distant from the typical value, and therefore, more dispersed.
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7 0

2 years ago

Show all your work. Indicate clearly the methods you use, because you will be scored on the correctness of your methods as well

laiz [17]

Answer:

The value is $P(A) = 0.133617$

Step-by-step explanation:

From the question we are told that

The mean is $\mu = 7.5$

The standard deviation is $\sigma = 0.2$

The safest water level is between 7.2 and 7.8

Generally the probability that the selected pool has a pH level that is not considered safe is mathematically represented as

$P(A) = 1 - P(7.2 \le X \le 7.8 )$

Here

$P(7.2 < X < 7.8 ) = P(\frac{ 7.2 - \mu }{\sigma } < \frac{X - \mu }{ \sigma }$

Generally $\frac{X - \mu }{ \sigma } = Z (The \ standardized \ value \ of X )$

So

$P(7.2 < X < 7.8 ) = P(\frac{ 7.2 - 7.5 }{0.2 } < Z$

$P(7.2 < X < 7.8 ) = P(-1.5 < Z$

=> $P(7.2 < X < 7.8 ) = P(Z < 1.5) - P( Z < - 1.5)$

From the z-table the probability of (Z < -1.5) and ( Z <1.5) are

$P(Z < 1.5) = 0.93319$

and

$P(Z < -1.5) = 0.066807$

So

$P(7.2 < X < 7.8 ) =0.93319 - 0.066807$

$P(7.2 < X < 7.8 ) =0.0866383$

So

$P(A) = 1 - 0.0866383$

=> $P(A) = 0.133617$

5 0

2 years ago

According to the Rational Root Theorem, which function has the same set of potential rational roots as the function g(x) = 3x5 –

SVETLANKA909090 [29]

We have to identify the function which has the same set of potential rational roots as the function $g(x)= 3x^5-2x^4+9x^3-x^2+12$ .

Firstly, we will find the rational roots of the given function.

Let 'p' be the factors of 12

So, p= $\pm 1, \pm 2, \pm 3, \pm 4, \pm 6$

Let 'q' be the factors of 3

So, q= $\pm 1, \pm 3$

So, the rational roots are given by $\frac{p}{q}$ which are as:

$\pm 1, \pm 2, \pm 3, \pm 4, \pm 6, \pm \frac{1}{3}, \pm \frac{2}{3}, \pm \frac{4}{3}$ .

Consider the first function given in part A.

f(x) = $3x^5-2x^4-9x^3+x^2-12$

Here also, Let 'p' be the factors of 12

So, p= $\pm 1, \pm 2, \pm 3, \pm 4, \pm 6$

Let 'q' be the factors of 3

So, q= $\pm 1, \pm 3$

So, the rational roots are given by $\frac{p}{q}$ which are as:

$\pm 1, \pm 2, \pm 3, \pm 4, \pm 6, \pm \frac{1}{3}, \pm \frac{2}{3}, \pm \frac{4}{3}$ .

Therefore, this equation has same rational roots of the given function.

Option A is the correct answer.

4 0

2 years ago

Read 2 more answers

Consider the continuous random variable X, which has a uniform distribution over the interval from 20 to 28.

anastassius [24]

Answer:

a) The probability distribution is $f(x) = \frac{1}{8}$

b) 0.5 = 50% probability that X will take on a value between 21 and 25.

c) 0.25 = 25% probability that X will take on a value of at least 26.

Step-by-step explanation:

Uniform probability distribution:

An uniform distribution has two bounds, a and b.

The probability of finding a value of at lower than x is:

$P(X < x) = \frac{a - x}{b - a}$

The probability of finding a value between c and d is:

$P(c \leq X \leq d) = \frac{d - c}{b - a}$

The probability of finding a value above x is:

$P(X > x) = \frac{b - x}{b - a}$

Uniform distribution over the interval from 20 to 28.

This means that $a = 20, b = 28$

a. What’s the probability density function?

The probability density function of the uniform distribution is:

$f(x) = \frac{1}{b - a}$

In this question:

$f(x) = \frac{1}{28 - 20} = \frac{1}{8}$

b. What’s the probability that X will take on a value between 21 and 25?

$P(21 \leq X \leq 25) = \frac{25 - 21}{28 - 20} = \frac{4}{8} = 0.5$

0.5 = 50% probability that X will take on a value between 21 and 25.

c. What’s the probability that X will take on a value of at least 26?

$P(X > 26) = \frac{28 - 26}{28 - 20} = \frac{2}{8} = 0.25$

0.25 = 25% probability that X will take on a value of at least 26.

4 0

2 years ago

Perry, maria, and lorna are painting rooms in a college dormitory. working alone, perry can paint a standard room in 3 hours, ma

Leviafan [203]

Answer:Perry and Lorna take the maximum time and Maria and Lorna take the minimum time when they work together.

Explanation: Since, according to the question- Perry takes time when he works alone = 3 hours

Similarly, Maria takes = 2 hours, While Lorna takes= 2 hours 30 minutes or 2.5 hours.

since, there are three people thus their are three possibility to choose any two of them.

1- when Perry and Maria work together then time taken by them is $\frac{1}{1/2+1/3}$ = $\frac{1}{5/6}$ = 6/5= 1 hour 12 minutes.

2- when Maria and Lorna work together then time taken by them is $\frac{1}{1/2 + 1/2.5}$ = 10/9= 1 hours 1/9 minutes ≈ 1 hours 7 min

3- when Perry and Lorna work together then time taken= $\frac{1}{1/3+1/2.5}$ = 15/11= 1 hour 4/11 minutes≈ 1 hours 21 minutes

From the above explanation, it has been proved that when we talk about 2 members team then Perry and Lorna take the maximum time. While Maria and Lorna take the minimum time when they work together.

3 0

2 years ago

Read 2 more answers