Question

The ages of 20 students travelling to Dharamshala on an educational trip are as follows :-
14, 15, 14, 15, 15, 16, 16, 13, 15, 15, 15, 14, 12, 13, 14, 15, 16, 13, 14, 14.
Find the number of students whose age is less than 15 years.​

Answer 1

Answer:

I think its seventeen(17)

Answer 2

Answer:

I think it will be helpful for you.

Step-by-step explanation:

There are 15 students in the class. Each student has the same chance to be chosen.

Therefore, the probability of each student to be selected is

15

1

.

The given information can be compiled in the frequency table as follows.

P(X=14)=

15

2

,P(X=15)=

15

1

,P(X=16)=

15

2

,P(X=16)=

15

3

,P(X=18)=

15

1

,P(X=19)=

15

2

,P(X=20)=

15

3

,P(X=21)=

15

1

Therefore, the probability distribution of random variable X is as follows.

Then, mean of X=E(X)

=∑X

i

P(X

i

)

=14×

15

2

+15×

15

1

+16×

15

2

+17×

15

3

+18×

15

1

+19×

15

2

+20×

15

3

+21×

15

1

=

15

1

(28+15+32+51+18+38+60+21)

=

15

263

=17.53

E(X

2

)=∑X

i

2

P(X

i

)

=(14)

2

⋅

15

2

+(15)

2

⋅

15

1

+(16)

2

⋅

15

2

+(17)

2

⋅

15

3

+(18)

2

⋅

15

1

+(19)

2

⋅

15

2

+(20)

2

⋅

15

3

+(21)

2

⋅

15

1

=

15

1

⋅(392+225+512+867+324+722+1200+441)

=

15

4683

=312.2

∴ Variance (X)=E(X

2

)[E(X)]

2

=312.2−(

15

263

)

2

=312.2−307.4177

=4.7823

≈4.78

Standard deviation =

Variance(X)

=

4.78

=2.186

≈2.19

like and marks as brilliant plz