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
ella [17]
3 years ago
8

A four year old is going to spin around with his arms stretched out 100 times. From past experience, his father knows it takes a

pproximately 1/2 second to perform one full spin, with a standard deviation of 1/3 second. What is
the approximate probability that it will take this child over 55 seconds to complete spinning?
Mathematics
1 answer:
Sati [7]3 years ago
6 0

Answer:

P(X \geq0.55) \leq 0.22

Step-by-step explanation:

Using central Limit Theorem (CLT), The sum of 100 random variables;

Y=X_1+X_2+...+X_{100} is approximately normally distributed with

Y ~ N (100 × \frac{1}{3^2} ) = N ( 50, \frac{100}{9} )

The approximate probability that it will take this child over 55 seconds to complete spinning can be determined as follows;

N ( 50, \frac{100}{9} )

P(Y>55) =P(Z>\frac{55-50}{10/3})

P(Y>55) =P(Z>1.5)

P(Y>55) =\phi (-1.5)

P(Y>55) =0.0668

Using Chebyshev's inequality:

P(|X-\mu\geq K)\leq \frac{\sigma^2}{K^2}

Let assume that X has a symmetric distribution:

Then:

2P(X-\mu\geq K)\leq) \frac{\sigma^2}{K^2}

2P(X \geq \mu+K)\leq) \frac{\sigma^2}{K^2}

2P(X\geq0.5+0.05)\leq \frac{\frac{1}{\frac{3^2}{100} } }{0.05^2}               where: (\sigma^2 = \frac{1}{3^2/100})

P(X \geq0.55) \leq 0.22

You might be interested in
The number of E.coli bacteria cells in a pond of stagnant water can be represented by the function below, where A represents the
liq [111]

Answer:

  • <u>Option B. 59%</u>

Explanation:

The function that represents the number of E.coli bacteria cells per 100 mL of water as the time t years elapses is:

  • A(t)=136(1.123)^{4t}

The base, 1.123, represents the multiplicative constant rate of change of the function, so you just must substitute 1 for t in the power part of the function:

  • rate=(1.123)^{4t}=(1.123)^4=1.590

Then, the multiplicative rate of change is 1.590, which means that every year the number of E.coli bacteria cells per 100 mL of water increases by a factor of 1.590, and that is 1.59 - 1 = 0.590 or 59% increase.

8 0
3 years ago
10) Which two ratios form a proportion? A) 1 : 2 and 4 : 2 B) 1 : 2 and 6 : 3 C) 2 : 1 and 2 : 4 D) 2 : 1 and 6 : 3
Likurg_2 [28]

Answer:

2/1and6/3 because if you do cross multilication they both equal 6

Step-by-step explanation:

8 0
3 years ago
Simplify.<br> 5V18-2V50<br> V50
NISA [10]

Answer:

-500

Step-by-step explanation:

7 0
3 years ago
What is the domain of the given function?
kari74 [83]
B would be the correct answer
5 0
3 years ago
What was the name of the small group of Jews that was especially opposed to Hellenism and Roman rule? A. Zealots B. Martyrs C. G
Klio2033 [76]
The answer is A. Zealots

4 0
3 years ago
Read 2 more answers
Other questions:
  • P and q are on a number line. If p has a coordinate -5 and pq =7 , what could the coordinate of p be
    10·1 answer
  • Which two senses are considered "chemical senses"?
    9·2 answers
  • CN someone help me with this
    5·1 answer
  • Rewrite in mathematical language. Every negative integer J is less than or equal to its inverse.
    13·1 answer
  • Would 3×1/8 be 3/8 is this right can somebody help me with this plz
    14·2 answers
  • An auditorium with 52 rows is laid out where 6 seats comprise the first row, 9 seats comprise the second row, 12 seats comprise
    8·2 answers
  • the sum of three numbers is 116. The first number is 6 more than the third. The second number is 3 times the third. What are the
    9·1 answer
  • What is the present value of 6000 received 14 years from today when the interest rate is 10%
    14·1 answer
  • This hyperbola is centered at the origin. Find its equation. Foci: (-9,0) and (9,0) Vertices: (-2,0) and (2,0)
    6·1 answer
  • Varun’s neighborhood is having a Halloween party. His family donated 9 bags of candy with 115 pieces in every bag. Christy’s fam
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!