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
Alexandra [31]
2 years ago
15

Suppose that 50% of the watches produced by a certain factory are defective. A store buys a box with 400 watches produced by thi

s factory. Assume That this is a random sample.(a) Write an expression for the exact probability that at least 215 watches out ofthe 400 are defective. You do not need to numerically evaluate it.(b) Argue whether the normal or the Poisson approximation is appropriate to es-timate the above probability and then estimate it.
Mathematics
1 answer:
tiny-mole [99]2 years ago
4 0

Answer:

(a)\ P(x \ge 215)

(b)\ P(x \ge 214.5) = 0.07353

Step-by-step explanation:

Given

p = 0.50 ---- proportion of watches with defects

n = 400 --- Number of watches

Solving (a): Represent at least 215 of 400 are defective

In inequalities, at least means: \ge

So, the probability is represented as: P(x \ge 215)

Solving (b): Calculate P(x \ge 215)

Normal or Poisson: Normal distribution is characterized by 2 parameters \mu and \sigma.

These two parameters can be easily calculated from the given parameters in the question. So, we solve using normal distribution

Start by calculating the mean

\mu =np

\mu = 0.50 * 400

\mu = 200

Calculate standard deviation

\sigma = \sqrt{\mu (1 - p)

\sigma = \sqrt{200 * (1 - 0.50)

\sigma = \sqrt{200 *  0.50

\sigma = \sqrt{100

\sigma = 10

By continuity correction, we have:

x \to x - 0.5

x \to 215 - 0.5

x \to 214.5

So, we have:

P(x \ge 215) = P(x \ge 214.5)

Calculating P(x \ge 214.5), we have:

P(x \ge 214.5) = 1 - P(x < z)

Calculate z score

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

z = \frac{214.5 - 200}{10}

z = \frac{14.5}{10}

z = 1.45

So, we have:

P(x \ge 214.5) = 1 - P(x < 1.45)

Using the z score probability table, we have:

P(x < 1.45) = 0.92647

So, we have:

P(x \ge 214.5) = 1 - 0.92647

P(x \ge 214.5) = 0.07353

You might be interested in
Help please!!!!<br> Solve the system by graphing
kotegsom [21]

Answer:

picture of graph is attached. lmk if ur getting these right. its been a while since I've dont this

7 0
3 years ago
2(m-n^2)-6(n^2+3m) simplify by like terms
umka2103 [35]
2(m-n^2)-6(n^2+3m)
=2m-2n^2-6n^2+18m
=20m-8n^2


Done ✅ Hope it helps
5 0
3 years ago
the Honda CRV gets 37 miles per gallon on average how much carbon dioxide will be admitted if the Honda were driven 400 miles
Pani-rosa [81]

According to the equation located here: https://www.1728.org/glwarmng.htm burning one gallon of gasoline produces 19.3 pounds of carbon dioxide.

So, if a car gets 37 miles per gallon and if it travels 400 miles, it will use 10.81 gallons of gasoline and will produce 19.3 * 10.81 = 208.63 pounds of carbon dioxide.



6 0
3 years ago
Using the triangle below, find the value of x.
xenn [34]

Answer:

b

Step-by-step explanation:

it looks like the right anwser

3 0
3 years ago
An equation is shown below: 8x + 2(x - 7) = 7x + 3x - 14 Part A: Solve the equation and write the number of solutions. Show all
Art [367]
8x+2(x-7)=7x+3-14\\8x+2x-14=7x+3-14~~Distributive~property\\10x-14=7x-11~combine~like~terms\\&#10;3x-14=-11~subtract~the~7x~from~both~sides\\&#10;3x=3~add~14~to~both~sides\\x=1~divide~both~sides~by~3
8 0
3 years ago
Read 2 more answers
Other questions:
  • The diameter of the larger circle is 12.5 cm. The diameter of the smaller circle is 3.5 cm.
    7·1 answer
  • Maricel is programming an archery component of a new video game. In her code, she has created an "auto aim" feature that helps p
    11·2 answers
  • in a right triangle the sum of the squares of the leg lengths is equal to the square of the hypotenuse length what does this des
    15·2 answers
  • Consider The Graph shown?
    11·1 answer
  • PLEASE HELP ASAP!!! Take 2y 2 - 3y - 5 from y 3 - 6y 2 + 5y. Select the correct answer.
    6·1 answer
  • Marta wants to purchase charms for her necklace. Each charm cost $1.59. She wants to spend no more than $20 for the charms. Whic
    12·1 answer
  • A plant grew 3 1/4 inches over a 6 1/2 month period.what was the average monthly growth rate for the plant
    8·1 answer
  • Line r and m are parallel. Find the value of x.
    5·1 answer
  • Help me out on this question
    10·1 answer
  • Use the following figure to find the value of x <br>(plz help)​
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!