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
Dmitriy789 [7]
3 years ago
12

It is known that 45% of senior citizens are deficient in vitamin D. Let Y be the number of vitamin D efficient individuals in a

random sample of n = 15 senior citizens. (a) Calculate P(Y = 5). Also obtain an approximation for this probability using the normal approximation. (b) Calculate P(Y > 7). Also obtain normal approximations for this probability with and without using continuity correction. (c) Calculate P(4
Mathematics
1 answer:
Mashutka [201]3 years ago
8 0

Answer:

a ) 0.1403604645 and 0.1368

b) 0.3464961 and 0.3485

c) 0.802671982 and 0.8018

Step-by-step explanation:

Y~ B (15,0.45)

Y~ N (15*0.45, 15*0.45*0.55) = Y~ N (6.75, 3.7125)

a) P(Y=5) = 15C5 (0.45)^5 * (0.55)^10 = 0.1403604645

   For normal approximation

P(Y = 5 ) = P ( 4.5 < Y < 5.5 )  ......... continuity correction

Hence,

P ( 4.5 < Y < 5.5 ) = P ( \frac{4.5 - 6.75}{\sqrt{3.7125} }  < Z < \frac{5.5 - 6.75}{\sqrt{3.7125} } ) = P ( -1.16775 < Z < -0.64875 )

The probability P ( 4.5 < Y < 5.5 ) = 0.1368

b) P(Y>7) = 15C8 (0.45)^ 8 (0.55)^7 + 15C9 (0.45)^9 * (0.55)^6 + 15C10 (0.45)^10 * (0.55)^5 + 15C11 (0.45)^11 * (0.55)^4 + 15C12 (0.45)^12 * (0.55)^3 + 15C13 (0.45)^13 * (0.55)^2 + 15C14 (0.45)^14 * (0.55) + (0.45)^15

= 0.3464961

  For normal approximation

P(Y > 7 ) = P (Y > 7.5 )  ......... continuity correction

Hence,

P (Y > 7.5) = P (Z > \frac{7.5-6.75}{\sqrt{3.7125} } ) = P (Z > 0.389249)\\

The probability P ( Y>7.5 ) = 0.3485

c) P (4 < Y < 10) = 15C5 (0.45)^5 (0.55)^10 + 15C6 (0.45)^ 6 (0.55)^9 + 15C7 (0.45)^7 (0.55)^8 + 15C8 (0.45)^ 8 (0.55)^7 + 15C9 (0.45)^9 * (0.55)^6

= 0.802671982

For normal approximation

P( 4 < Y < 10 ) = P (4.5< Y < 9.5 )  ......... continuity correction

Hence,

P ( 4.5 < Y < 9.5 ) = P ( \frac{4.5 - 6.75}{\sqrt{3.7125} }  < Z < \frac{9.5 - 6.75}{\sqrt{3.7125} } ) = P ( -1.167748416 < Z < 1.427248064 )

The probability P (4.5< Y < 9.5 ) = 0.8018

You might be interested in
Identify The range of the functions shown in the graph
alexandr402 [8]
A
y \\ is \:  all \: real \: numbers
3 0
3 years ago
Read 2 more answers
What is the area of Vivian’s garage door?
sergey [27]

The area  of Vivian’s garage door is 62.5 square feet

<h3>Area of composite shape.</h3>

The Vivian garage is made up of a trapezoid and a rectangle. The area of the door is expressed as;

Area = Area of rectangle + area of trapezoid

Area = (5 * 8) + 0.5(7 + 8)*3
Area= 40 +22.5
Area = 62.5 square feet

Hence the area  of Vivian’s garage door is 62.5 square feet

Learn more on composite shapes here: brainly.com/question/8370446

#SPJ1

3 0
1 year ago
Factorize: x² + 3x + 2​
zvonat [6]

Step-by-step explanation:

x² + 3x + 2

x² + x + 2x + 2 because 1+2=3 and 2×1=2

By taking out common terms, we get

x(x+1)+2(x+1)

(x+1)(x+2)

7 0
3 years ago
Solve this and show work​
just olya [345]

Answer:

1.71

Step-by-step explanation:

x/4 = 3/7

4 * 3 = 12

12/7 = 1.714285714285714

Rounded to the nearest hundreths, the answer is  1.71

6 0
2 years ago
Ying Zyiyu covers the first 300 miles of a trip traveling at 60 mph. and the last hundred miles traveling at 40 mph. What was hi
UNO [17]

Answer:

53.33 mph

Step-by-step explanation:

Speed is the rate of change of distance with time. Mathematically,

speed = distance/time

and is measured in miles per hour or meter per second.

To get the average speed over the entire trip, we must get the total time  spent on trip and the total distance, then apply the speed formula

Time for the first 300 miles

= 300/60

= 5 hours

Time spent on the last 100

= 100/40

= 2.5 hours

Total time of the trip = 5 + 2.5

= 7.5 hours

Total distance covered

= 300 miles + 100 miles

= 400 miles

Average speed on the trip

= 400/7.5

= 53.33 miles per hour

7 0
3 years ago
Other questions:
  • Which is a factor of 3x^2 − 33x + 84?
    7·1 answer
  • Factoring x squared -36
    7·1 answer
  • If set A = {3, 4, 7, 9} and if set D = {9, 4, 3, 7}, A = D.<br><br> True<br> False
    7·2 answers
  • Which fraction is the largest 5/7 7/10 10/13 show how u worked out the answer
    9·1 answer
  • What is the shape of a cross section formed when a triangular prism is sliced by a plane vertical to its base?
    14·1 answer
  • Multiple choice question
    6·1 answer
  • Find x in the following equation 2x^{2} +4=0
    13·1 answer
  • Please help, I need the answer
    15·2 answers
  • Pls help me. To be submitted tomorrow​
    10·1 answer
  • Below is the frequency distribution of the weights (in kg) of some sample of teen-agers.
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!