The age of children in kindergarten on the first day of school is uniformly distributed between 4.8 and 5.84 years old. A first time kindergarten child is selected at random. Round answers to 4 decimal places if possible.The mean of this distribution is The standard deviation is The probability that the the child will be older than 5 years old?

Question
Asked Nov 9, 2019

The age of children in kindergarten on the first day of school is uniformly distributed between 4.8 and 5.84 years old. A first time kindergarten child is selected at random. Round answers to 4 decimal places if possible.

  1. The mean of this distribution is 
  2. The standard deviation is 
  3. The probability that the the child will be older than 5 years old? 
check_circleExpert Solution
Step 1

1.

 

The mean of the distribution is 5.3200 and it is obtained below:

 

 

From the given information, the random variable X as age of the children in kindergarten on the first day of school is uniformly distributed between 4.8 and 5.84 years old. That is, a=4.8 and b=5.84.

 

The probability density function for X is,

1
f (x)
b-a
1
5.84-4.8
4.8 X 5.84
0.961538
b+a
E(X)
5.84 4.8
2
=5.32
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1 f (x) b-a 1 5.84-4.8 4.8 X 5.84 0.961538 b+a E(X) 5.84 4.8 2 =5.32

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Step 2

2.

 

The standard deviation is 0.3002 and it ...

(b-a)
SD(X)
12
(5.84-4.8)
12
=0.3002
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(b-a) SD(X) 12 (5.84-4.8) 12 =0.3002

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