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The age of children in kindergarten on the first day of school is uniformly distributed between 4.87 and 5.85 years old. A first time kindergarten child is selected at random. Round answers to 4 decimal places if possible.I JUST NEED HELP ON #3 AND #5The mean of this distribution isThe standard deviation isThe probability that the the child will be older than 5 years old?The probability that the child will be between 5.17 and 5.57 years old isIf such a child is at the 65th percentile, how old is that child? years old.

Question

The age of children in kindergarten on the first day of school is uniformly distributed between 4.87 and 5.85 years old. A first time kindergarten child is selected at random. Round answers to 4 decimal places if possible.

I JUST NEED HELP ON #3 AND #5

  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?
  4. The probability that the child will be between 5.17 and 5.57 years old is
  5. If such a child is at the 65th percentile, how old is that child? years old.

 

check_circleAnswer
Step 1

A uniform distribution has an equal probability for all the outcomes of the random variable, that is, it has a constant probability. A uniform distribution is defined over the range (a, b) where a is the smallest value and b is the largest value of the distribution. The values, (a, b) are the parameters of the uniform distribution.

Step 2

(3)

Consider, X be the random variable which represents the age of the children in kindergarten on the first day of school is uniformly distributed with parameters a= 4.87 and b=5.85.

The probability that children will be older than 5 years can be calculated as:

5.85
1
P(X 5)
5.85 4.87
1
15.85
0.98
1
(5.85-5)
0.98
=0.867
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5.85 1 P(X 5) 5.85 4.87 1 15.85 0.98 1 (5.85-5) 0.98 =0.867

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Step 3

(5)

Percentiles of the continuous uniform distribution on the interv...

—а+(b-а)р
Where
p is percentile
help_outline

Image Transcriptionclose

—а+(b-а)р Where p is percentile

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