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xx18181919202021212222F(x)F(x)202033994444Let xx be the ages of students in a class. Given the frequency distribution F(x)F(x) above, determine the following probabilities:(a) P(x≥21 or x<19)=P(x≥21 or x<19)= equation editorEquation Editor (b) P(x≤21)=P(x≤21)= equation editorEquation Editor (c) P(x<22)=P(x<22)=

Question
xx 1818 1919 2020 2121 2222
F(x)F(x) 2020 33 99 44 44



Let xx be the ages of students in a class. Given the frequency distribution F(x)F(x) above, determine the following probabilities:

(a) P(x≥21 or x<19)=P(x≥21 or x<19)= 

equation editor
Equation Editor

 

(b) P(x≤21)=P(x≤21)= 

equation editor
Equation Editor

 

(c) P(x<22)=P(x<22)=

check_circleAnswer
Step 1

From the given frequency distribution, the corresponding probabilities are given in the below table.

F(x)
РX-x)
20 1
Р(X -18) -
18
20
40 2
3
Р(х -19) -
40
19
3
9
P(X 20
40
20
9
4
1
P(X 21
21
40
10
4
P(X 22)
22
4
40 10
Total
40
1
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Image Transcriptionclose

F(x) РX-x) 20 1 Р(X -18) - 18 20 40 2 3 Р(х -19) - 40 19 3 9 P(X 20 40 20 9 4 1 P(X 21 21 40 10 4 P(X 22) 22 4 40 10 Total 40 1

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Step 2

a).

The required probability can be obtained as follows.

P(x221 or x <19)P(X =18)+P(X 21)+P(X=22)
11 1
2 10 10
=0.7
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Image Transcriptionclose

P(x221 or x <19)P(X =18)+P(X 21)+P(X=22) 11 1 2 10 10 =0.7

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Step 3

b).

The required probability can b...

P(x21) P(X 18)+P(X =19)+P(X=20)+ P(X 21)
9 1
1 3
2 40 40 10
=0.9
help_outline

Image Transcriptionclose

P(x21) P(X 18)+P(X =19)+P(X=20)+ P(X 21) 9 1 1 3 2 40 40 10 =0.9

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