1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Blizzard [7]
3 years ago
13

Chapter 7, Section 7.2, Question P9 The process for manufacturing a ball bearing results in weights that have an approximately n

ormal distribution with mean 0.15 g and standard deviation 0.005 g. a. If you select one ball bearing at random, what is the probability that it weighs less than 0.149 g? (round to four decimal places) b. If you select four ball bearings at random, what is the probability that their mean weight is less than 0.149 g? (round to four decimal places) c. If you select ten ball bearings at random, what is the probability that their mean weight is less than 0.149 g? (round to four decimal places)
Mathematics
1 answer:
bogdanovich [222]3 years ago
8 0

a. Let X be a random variable representing the weight of a ball bearing selected at random. We're told that X\sim\mathcal N(0.15,0.005^2), so

\mathrm P(X

where Z\sim\mathcal N(0,1). This probability is approximately

\mathrm P(Z

b. Let X_i be a random variable representing the weight of the i-th ball that is selected, and let Y be the mean of these 4 weights,

Y=\dfrac{X_1+X_2+X_3+X_4}4

The sum of normally distributed random variables is a random variable that also follows a normal distribution,

X_1+X_2+X_3+X_4\sim\mathcal N(4\cdot0.15,4\cdot0.005^2)

so that

Y\sim\mathcal N(0.15,0.005^2)

Then

\mathrm P(Y

c. Same as (b).

You might be interested in
Sloane kicked a soccer ball off the ground at a speed of 36 feet per second. the height of the ball can be represented by the fu
deff fn [24]

The total time in seconds the ball will take to travel before returning the ground is 2.25 seconds.

<h3>What is factorisation?</h3>

The breaking or breakdown of an entity (such as an integer, a matrices, or a polynomials) into a products of another unit, or factors, whose multiplication results in the original number, matrix, etc., is known as factorisation or factoring in mathematics. 

Calculation for the time;

Let 't' be the time in second the ball will travel.

Let H(t) be the total height travelled by the ball.

The equation of the height is given as

H(t)=-16 t^{2}+36 t

As soon as the ball will return to the ground the total height will become zero.

So, put equation of height equal to zero.

-16 t^{2}+36 t=0

Factorise the above equation;

-16 t\left(t-\frac{9}{4}\right)=0

Put each value equals to zero to get the value of time.

\begin{aligned}&t=0 \mathrm{sec} \\&t=9 / 4=2.25 \mathrm{sec}\end{aligned}

As, time can not be zero

Therefore, the total time taken by the ball to return to the ground is 2.25 sec.

To know more about factorisation, here

brainly.com/question/25829061

#SPJ4

4 0
1 year ago
Jaquez earns money by doing yard work. It takes her an average of 3 hours to pull weeds and an average of 2.5 hours to mow the l
vodomira [7]

Answer:

Step-by-step explanation:

Let x = number of hours to pull weed in a day

Let y = number of hours to now lawn in a day

It takes her an average of 3 hours to pull weeds and an average of 2.5 hours to mow the lawn. She can work no more than 8 hours a day.

This means

3x + 2.5y is lesser than/ equal to 8

She charges $50 to weed and $65 to mow the lawn.

This means she charges

50x +65y

She needs to cover her expenses of $120 to make a profit. This means she needs to earn an amount greater than or equal to $120

50x + 65y greater than or equal to 120

4 0
3 years ago
What is the polynomial function of lowest degree with lead coefficient 1 and roots 1 and 1 + i? f(x) = x2 – 2x + 2 f(x) = x3 – x
konstantin123 [22]

Answer:

f(x)=x^{3}-3x^{2} +4x-2

Step-by-step explanation:

we know that

The <u><em>conjugate root theorem</em></u> states that if the complex number a + bi is a root of a polynomial P(x) in one variable with real coefficients, then the complex conjugate a - bi is also a root of that polynomial

In this problem we have that

The polynomial has roots 1 and (1+i)

so

by the conjugate root theorem

(1-i) is also a root of the polynomial

therefore

The lowest degree of the polynomial is 3

so

f(x)=a(x-1)(x-(1+i))(x-(1-i))

Remember that

The leading coefficient is 1

so

a=1

f(x)=(x-1)(x-(1+i))(x-(1-i))\\\\f(x)=(x-1)[x^{2} -(1-i)x-(1+i)x+(1-i^2)]\\\\f(x)=(x-1)[x^{2} -x+xi-x-xi+2]\\\\f(x)=(x-1)[x^{2} -2x+2]\\\\f(x)=x^{3}-2x^{2} +2x-x^{2} +2x-2\\\\f(x)=x^{3}-3x^{2} +4x-2

5 0
3 years ago
Read 2 more answers
Please help me with the Question thanks
Lelechka [254]
3/4 equals 21/24....
4 0
3 years ago
Read 2 more answers
the length of a rectangle is five times its width. if the area of the rectangle is 245 meters squared, find its perimeter
Vikentia [17]

Your answer is 84 meters.


We can call the width x, and thus the length 5x, and then we can say that 5x × x = 245, which simplifies to 5x² = 245, and then we can solve:


5x² = 245

÷ 5

x² = 49

√

x = 7


Now that we know what x is, we can find the perimeter by using it as the width, and then multiplying it by 5 to find its length. This gives us:


(7 × 2) + (5 × 7 × 2) = 14 + (35 × 2) = 14 + 70 = 84


So your answer is 84 meters.


I hope this helps!

6 0
3 years ago
Other questions:
  • Write two irrational numbers between 1 and 2
    11·2 answers
  • Which equation is modeled below?
    13·1 answer
  • Find the minimum and maximum of f(x,y,z)=x^2+y^2+z^2 subject to two constraints, x+2y+z=4 and x-y=8.
    7·1 answer
  • Use the Rational Root Theorem to list all possible rational roots of the polynomial equation x3 – x2 – x – 3 = 0. Do not find th
    10·2 answers
  • I need help with finding x<br> ANSWER ASAP!!!!!!!!!!
    8·1 answer
  • - Write 1.359 X 105 in standard form.
    12·1 answer
  • Ano ang area ng isang maliit na parisukat​
    6·1 answer
  • one of the same side exterior angles of two parallel lines is 20 degrees less than the other same side exterior angle find the m
    5·1 answer
  • There are 12 teams, each representing a different country, in a women’s olympic basketball tournament. in how many ways is it po
    12·1 answer
  • One number is six more than the other number . thesum of their squares is 90
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!