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dexar [7]
3 years ago
7

Bottling cola A bottling company uses a filling machine to fill plastic bottles with cola. The bottles are supposed to contain 3

00 milliliters (ml). In fact, the contents vary according to a Normal distribution with mean μ = 298ml and standard deviation σ = 3ml.
What is the probability that a randomly selected bottle contains less than 295 ml? Show your work.
Mathematics
1 answer:
erik [133]3 years ago
4 0

Answer:

P(X

And we can find this probability using the normal standard table or excel:

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".  

Solution to the problem

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

X \sim N(298,3)  

Where \mu=298 and \sigma=3

We are interested on this probability

P(X

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:

P(X

And we can find this probability using the normal standard table or excel:

P(Z

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Given the recursive formula below, what are the first four terms of the sequence
Ivan

Answer:

c

Step-by-step explanation:

8 0
2 years ago
In a movie theater, the number of seats in a row is 8 greater than the total number of rows. How many rows are in the movie thea
Harman [31]

Answer:

26 rows

Step-by-step explanation:

this is like a rectangle length×width situation.

seats per row = s

number of rows = r

s × r = 884

s = r + 8

so, we can use e.g. the second equation in the first :

(r + 8) × r = 884

r² + 8r = 884

r² + 8r - 884 = 0

the general solution to such a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = r

a = 1

b = 8

c = -884

r = (-8 ± sqrt(8² - 4×1×-884))/(2×1) =

= (-8 ± sqrt(64 + 3536))/2 = (-8 ± sqrt(3600))/2 =

= (-8 ± 60)/2 = -4 ± 30

r1 = -4 + 30 = 26

r2 = -4 - 30 = -34

a negative number did not make any sense for the number of rows, so r = 26 is our answer.

8 0
1 year ago
I need help with # 14 and 15 ASAP... It is due tomorrow ..can some one please help me with it
Angelina_Jolie [31]

Answer:

See explanation

Step-by-step explanation:

A. Gasoline fill-up fee = $4.50

Cost per hour = $40

Average cost = C

Number of hours the scootcar is rented = h

Cost per h hours = $40h

Total cost = $40h + $4.50

Hence,

C = 40h+4.5

B. To plot the graph of the function, find h- and C- intercepts.

When h = 0, then C = 4.5, and we have point (0,4.5)

When C = 0, then 0 = 40h + 4.5, h = -45/400 = -0.1125, and we have point (-0.1125,0)

Plot these two points and connect them with a straight line.

Graph is attached, but you should take only that part of the graph that corresponds to points with h > 0, because the number of hours cannot be negative

8 0
3 years ago
Which statement best describes the polynomial
Stels [109]

Answer:

B

Step-by-step explanation:

Standard form is written according to the highest exponent on the variable to the lowest. This expression has exponents that descend from 8 to 7 and to 1. B is the correct solution.

6 0
3 years ago
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Check all that apply.
k0ka [10]

Answer:

C. -6x+15

A. First Picture

Step-by-step explanation:

We are given the inequality, -3(2x-5).

On simplifying the inequality, we get,

-3(2x-5)

i.e. -6x+15

i.e. -x

i.e. x>5

So, we get the correct representations of the inequality are,

C. -6x+15

A. the First Picture

5 0
2 years ago
Read 2 more answers
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