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
Zielflug [23.3K]
2 years ago
10

The mass of the eggs laid by a certain breed of hen is a normally distributed random variable with mean 0.06kg and standard devi

ation 0.009kg. If a random sample of 1800 eggs are sold, how many would you expect to have mass; (i)Less than 0.052 kg (standard size). (ii)Between 0.052 kg and 0.075kg (medium size).(iii)Greater than 0.075 kg (large size).
(b)If the cost of producing an egg in (a) is Gh¢0.45 and selling price of each standard, medium and large size eggs are Gh¢0.60, Gh¢0.80, and Gh¢0.95 respectively, calculate (i)The expected profit to be made from selling the standard size, medium size and large size eggs. (ii)The overall profit.​
Mathematics
1 answer:
Olin [163]2 years ago
3 0

a (i) The number of standard size is 288 eggs

a (ii) The number of medium size is 1,476 eggs

a (iii) The number of large size is 36 eggs

b (i) The expected profit made from selling the standard size is Gh¢43.2

b (ii) The expected profit made from selling the medium size is Gh¢516.6

b (iii) The expected profit made from selling the large size is Gh¢16.2

The given parameters:

the mean of the distribution, m = 0.06 kg

standard deviation (std) of the distribution, d = 0.009 kg

number of the samples, n = 1800 eggs

(i) Find the position of "less than 0.052 kg (standard size)":

  • 1 standard deviation below the mean = m - d
  • m - d = 0.06 kg  -  0.009 kg = 0.051 kg

(<em>the </em><em>standard size</em><em> is 1 standard deviation below the mean</em>)

  • less than 1 standard deviation below the mean in a normal distribution is equal to 16% of the data samples
  • Number of standard size = 0.16 x 1800 = 288 eggs

(ii) Find the position of "Between 0.052 kg and 0.075kg (medium size)":

  • 0.052 kg is 1 standard deviation below the mean
  • 2 standard deviation above the mean = m + 2d
  • m + 2d = 0.06 + 2(0.009) = 0.078 kg

(<em>the </em><em>medium size</em><em> is between 1 std below the mean and 2 std above the mean</em>)

  • Between 1 std below the mean and 2 std above the mean in a normal distribution = (68 + 14)% = 82%
  • Number of medium size = 0.82 x 1800 = 1,476 eggs

(iii) Find the position of "Greater than 0.075 kg (large size)":

  • 0.078 kg is 2 standard deviation below the mean
  • greater than 2 std above the mean in a normal distribution = 2 % of the data samples
  • Number of large size = 0.02 x 1800 = 36 eggs

<u>Check:</u> <em>288 eggs + 1476 eggs + 36 eggs = 1,800 eggs</em>

(b) the cost of production of an egg = Gh¢0.45

the selling price of the standard size = Gh¢0.60

the selling price of the medium size = Gh¢0.80

the selling price of the large size = Gh¢0.95

(i) The expected profit made from selling the standard size:

Profit = total revenue - cost of production

Profit = 288(0.6) - 288(0.45) = Gh¢43.2

(ii) The expected profit made from selling the medium size:

Profit = total revenue - cost of production

Profit = 1476(0.8) - 1476(0.45) = Gh¢516.6

(iii) The expected profit made from selling the large size:

Profit = total revenue - cost of production

Profit = 36(0.9) - 36(0.45) = Gh¢16.2

Learn more here: brainly.com/question/22520030

You might be interested in
A stamp gets more expensive each year. It increases in value by 60% each year what is the growth factor ?
bixtya [17]

Answer: Nancy spent $44.59 on 5.25 quarts of olive oil. What is the cost of one quart of olive oil? Round to the nearest cent.

$8.38 per quart

$8.49 per quart

$8.57 per quart

$8.92 per quart

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
10/r - 7 - 6b if r = 5 and b = -6
laiz [17]

Steps to solve:

10/r - 7 - 6b when r = 5 and b = -6

~Substitute

10/5 - 7 - 6(6)

~Simplify

5 - 7 + 36

~Subtract

-2 + 36

~Add

34

Best of Luck!

5 0
3 years ago
GEOMETRY!!!!!!!!!!!!!
Rina8888 [55]

(1,F)(2,C)(3,H)(4,A)(5,G)(6,G)(7,D)(8,B)(9,E)

You might want to review the words.

4 0
3 years ago
PLEASE HELP! TWO PROBLEMS!!
MrRissso [65]

1) x=−2 2) y=−6 Hopefully that helps you ❤.

6 0
3 years ago
What is 9m-28=2m explain
loris [4]
9m-28=2m
9m-28-2m=2m-2m
(9m-2m)-28=0
7m-28=0
7m-28+28=0+28
7m=28
(7m)/7 = 28/7
m=4
5 0
3 years ago
Read 2 more answers
Other questions:
  • I neeed help please ​
    12·1 answer
  • 1.Take 4x + 2 from 8x + 5.
    15·2 answers
  • If 3x - 1 = 11, what is the value of x2 + x?
    11·2 answers
  • 1) Which of the following represents a unit rate? *
    13·2 answers
  • Katie has a cold and needs to take one teaspoon
    10·1 answer
  • I will make brainlist if someone did an explanation.
    14·1 answer
  • AYUDA PLIS 1) Pablo compro un sobre de jugo que les costo $28,85, un alfajor por $85,50 y un helado. Si pago con $250 ¿Cuánto co
    14·1 answer
  • Is x = 5 a solution to the equation 19 - x = 14?
    12·2 answers
  • Find the value of x, y, and z.
    10·1 answer
  • What’s the answer for this…<br><br><br> Solve for p<br><br> 2p + 3 &gt; 2 (p – 3)
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!