A bottling company uses a filling machine to fill plastic bottles with cola. The bottles are supposed are supposed to contain 300m. In fact, the contents vary according to a Normal Distribution with mean of 298 mL and a standard deviation of 3 mL. (a) What is the probability that an individual bottle contains less than 295 mL? Show your work. (b) What is the probability that the mean contents of six randomly chosen bottles is less than 295 mL? Show your work.

Answer:

0.15866 ; 0.0071627

Step-by-step explanation:

Given that:

Mean (m) = 298

Standard deviation (s) = 3

A.) P(x < 295)

Using the relation to obtain the standardized score (Z) :

Z = (x - m) / s

Z = (295 - 298) / 3 = - 1

p(Z < - 1) = 0.15866 ( Z probability calculator)

B.)

Z = (x - m) / s /sqrt(n)

Z = (295 - 298) / 3/sqrt(6) = −2.449489

p(Z < - 2.449) = 0.0071627 ( Z probability calculator)

Given values are:

Mean,

Standard deviation,

(a)

P(x < 295)

The standardized score will be:

→ [tex]Z = \frac{(x-m)}{s}[/tex]

By substituting the values, we get

      [tex]= \frac{(295-298)}{3}[/tex]

      [tex]= \frac{-3}{3}[/tex]

      [tex]= -1[/tex]

Now,

By using the Z probability calculator, we get

→ [tex]p(Z< -1) = 0.15866[/tex]

(b)

The standardized score will be:

→ [tex]Z = \frac{x-m}{\frac{s}{\sqrt{n} } }[/tex]

By putting the values,

      [tex]= \frac{295-298}{\frac{3}{\sqrt{6} } }[/tex]

      [tex]= -2.449489[/tex]

Now,

→ [tex]p(Z < -2.449)= 0.007163[/tex]

Thus the responses above are correct.

Learn more about probability here:

https://brainly.com/question/20369155

3x– 2y = -3
y = 7 - 4x
Resolver por sustitución

please help i’ll give brainliest!!

What does the word Expressions mean in mathematics in your own words?

a fraction is shown 5/9 which number equivalent to the fraction

PLEASE HELP!!QUICK! in 3 years ,a gyms membership went up from 6,400 to 8,400.which expression shows how to find the percent of increase?
A.2,000 divide by 8,400
B.2,000 divide by 6,400
C.6,400 divide by 2,000

Find the slope of the lines that go through the following points.

which is not solution to the folloeing linear equality

A. (-2, 1)
B. (0, 0)
C. (2, -1)
D. (-9, -9)​

Write the quadratic equation in standard form:
3x – 17 + 3x^2= -4

What decimal number does point A on the number line below represent?

A vertical number line is shown from negative 2.00 to 0 to positive 2.00.There are tick marks to show increments of 1 over 4. Only the whole numbers are labeled. Point A is plotted at the third tick mark below 0.

−0.75
0.75
−1.25
1.25

бx +7= 8х - 15
Pls help will mark brainliest

Consider the enlarged triangle.

A smaller triangle has side lengths 4, 5, 3. A larger triangle has side lengths 8, 10, 6.

Which steps should be used to find the perimeter? Check all that apply.

Find the scale factor: enlarged over original = 6 over 3 = 2
Find the scale factor: enlarged over original = 3 over 6 = one-half
Calculate the perimeter of the original figure.
Divide the perimeter of the original figure by the scale factor.
Multiply the perimeter of the original figure by the scale factor.

10 flowers in 5 vases = ? flowers per vase

Rewrite y - 3 = 4(x + 2) in slope intercept form. Type in your answer without using any spaces. Example: y=-3/4x+12

solve the following system of equations y=2x+10. y=3x+12

PLS HELP ILL GIVE BRAINLIEST WHOEVER ANSWERS PLS :(

A survey was conducted of students at a high school and at a college to determine students' favorite subjects. The results are shown in the table.
History Math Science Total
High School 80 50 70 200
College 70
60
70 200
Total 150 110 140 400
What percentage of the students are college students that prefer history?
O A. 17.5%
OB. 35%
OC. 37.5%
D. 46.7%
E 75%

Each of three colored cups covers one of three objects. 1) The red cup is somewhere to the left of the white cup. 2) The coin is somewhere to the left of the bean. 3) The gray cup is somewhere to the right of the shell. 4) The bean is somewhere to the right of the gray cup. Under which color cup is the shell?

Which measurement is the best estimate for the length of a clothespin?

9 cm
9 km
9 mm
9 m

Dan invests £8200 into his bank account he receives 2% per year compound interest how much will Dan have after 7 years ?

what is 8 - 7 1/4 i need the answer fast

ana can swim at a rate of 3/8 mile in 1/3 hour.

the perimeter of a isosceles triangle is 5(2+root2) find the area

Direct Variation, Constant of Proportionality, and Constant Rate of Change all represent linear proportional relationships.

In the equation LaTeX: y=kx what does each variable represent.

Find the -intercept and -intercept of the line.

3x-7y=-21

x-intercept
y-intercept

Rochelle wants to use all of her raisins to bake batches of granola. She has 3/4 cup of raisins.
Each batch requires 1/8 cup of raisins. How many batches can she make?

Explain how to graph 5 2 on the number line. A number line going from 0 to 3. There are 2 equals spaces between each number. The number line contains 0, point A is one-half, 1, point B is 1 and one-half, point C is between point B and 2, 2, point D is 2 and one-half, 3.

To be a member of the choir, you must go to an audition. Henry's cousin is a member of the choir. What conjecture can you make about Henry's cousin?

A.) Henry’s cousin practices with the choir
B.) Henry is in the choir
C.) Henry’s cousin went to an audition

Pls help I’m timed on my test
what is the y- intercept of the linear function?
Y = -1/3 x + 1

Help will give crown

PLEASE ASAP QUICK THX​