Solve please. *Picture Included*

The manager of a local soft drink bottling company believes that a new beverage- dispensing machine, which is designed to dispen

Alexxandr [17]

Answer:

a) The mean is 7 ounces and the standard deviation is of 0.29 ounces.

b) 50% probability that x is at least 7 ounces.

c) 75% probability that x is between 6.5 and 7.25 ounces.

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 probability that we find a value X at least x is given by the following formula.

$P(X \geq x) = 1 - \frac{x - a}{b-a}$

The probability that we find a value X between c and d is given by the following formula.

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

The mean of the uniform distribution is:

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

The standard deviation of the uniform distribution is:

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

Anywhere between 6.5 and 7.5 ounces.

This means that $a = 6.5, b = 7.5$

(a) Find the mean and standard deviation of x.

Mean

$M = \frac{6.5 + 7.5}{2} = 7$

Standard deviation

$S = \sqrt{\frac{{7.5-6.5)^{2}}{12}} = 0.29$

The mean is 7 ounces and the standard deviation is of 0.29 ounces.

(b) Find the probability that x is at least 7 ounces.

$P(X \geq 7) = 1 - \frac{7 - 6.5}{7.5 - 6.5} = 0.5$

50% probability that x is at least 7 ounces.

(c) Find the probability that x is between 6.5 and 7.25 ounces.

$P(6.5 \leq X \leq 7.25) = \frac{7.25 - 6.5}{7.5 - 6.5} = 0.75$

75% probability that x is between 6.5 and 7.25 ounces.

7 0

3 years ago

the function f(x)= x+3 represents the length of a rectangle. the function g(x)=12x-5 represents the width of the rectangle. use

Juli2301 [7.4K]

Answer:

(f • g)(3) = 186

Step-by-step explanation:

The area of a rectangle is (length)(width).

Here, (length) = x + 3 and (width) = 12x - 5, and so the area as a function of x is

(f • g)(x) = (x + 3)(12x - 5) = 12x^2 - 5x + 36x - 15.

This simplifies to:

(f • g)(x) = (x + 3)(12x - 5) = 12x^2 + 31x - 15.

Evaluating this function at x = 3, as instructed, we get:

(f • g)(3) = (12)( - 5) = 12(3)^2 + 31(3) - 15.

Carrying out the indicated operations, we get: 108 + 93 - 15, or

(f • g)(3) = 186

6 0

3 years ago

Ive been stuck on this expression for a while now

natka813 [3]

Answer:

xy^(2)z^(6)

Step-by-step explanation:

i hope that helps you :)

4 0

4 years ago

C'est quoi un square root ?<br>

rosijanka [135]

Answer:

it defines an important concept of standard deviation used in probability theory and statistics. It has a major use in the formula for roots of a quadratic equation; quadratic fields and rings of quadratic integers, which are based on square roots, are important in algebra and have uses in geometry.

3 0

3 years ago

Read 2 more answers

Math is hard and suckssssssssssssssss

inessss [21]

Answer:

X=7

Hope it was helpful

Step-by-step explanation:

Good luck ^___^

4 0

3 years ago