Question
Asked Oct 4, 2019
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Suppose that the age of students at George Washington Elementary school is
uniformly distributed between 6 and 11 years old. 43 randomly selected children
from the school are asked their age. Round all answers to 4 decimal places where
possible
a. What is the distribution of X? X
U(
b. What is the distribution of ? & ~ N(
c. What is the probability that the average of 43 children will be between 8 and
8.4 years old?
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Suppose that the age of students at George Washington Elementary school is uniformly distributed between 6 and 11 years old. 43 randomly selected children from the school are asked their age. Round all answers to 4 decimal places where possible a. What is the distribution of X? X U( b. What is the distribution of ? & ~ N( c. What is the probability that the average of 43 children will be between 8 and 8.4 years old?

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Expert Answer

Step 1
  1. It is provided that the age of students is uniformly distributed between 6 and 11 years old. The randomly selected sample, n is 43.

The uniform distribution of X can be obtained as:

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X U (6,11)

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Step 2

The mean and standard deviation of X for the uniform distribution is,

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E(x)a+b 2 6+11 2 -8.5 S.D.(b-a V12 11-6 - 1.4434

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Step 3

b. The Central Limit Theorem states that if the sample size is greater than or equal to 30, the sampling distributions of the mean tend to be normal distribution, irre...

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E() E(x) 8.5 Var ()= Var(X) п (1.4434) 43 0.0484 S.D.() var() = 0.0484 0.22 Therefore, п TN(8.5,0.0336)

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