Question

The following table gives the distribution about weight of 38 students of a class:

Weight in kg	Number of students
31-35	9
36-40	5
41-45	14
46-50	3
51-55	1
56-60	2
61-65	2
66-70	1
71-85	1

Find the probability that weight of a student in the class is:
(i) at most 60 kg.
(ii) at least 36 kg.
(iii) not more than 50 kg.

Answer 1

We start solving the problem (i) by recalling the definition of at most in the given problem. We then find the total no. of students satisfying the criteria. After finding this we use the definition of probability to find the required result. Similarly, we recall the definition of at least in problem (ii) and not more than in problem (iii) at the start of solving and follow similar procedure as we did in problem (i).

Complete step by step answer:
According to the problem, we have a table showing a distribution about the weight of 38 students in the class. We need to find the probability that weight of a student in the class is:
(i) at most 60 kg.
(ii) at least 36 kg.
(iii) not more than 50 kg.

(i) We have given that the weight of a student in the class is at most 60 kg. This means that the maximum weight of the student should be 60 kg. So, this makes us find the probability that weight of a student in the class should be less than or equal to 60 kg.
Let us find the total no. of students in the class whose weight is less than or equal to 60 kg.
So, we have $\left( 9+5+14+3+1+2 \right)=34$ students weighing less than or equal to 60 kg in the class.
Now, we find the probability that the weight of a student in the class is at most 60 kg.
So, we have $\text{probability=}\dfrac{\text{no}\text{. of students weighing less than or equal to 60 kg}}{\text{Total no}\text{. of students in the class}}$.
$\Rightarrow \text{probability=}\dfrac{\text{34}}{\text{38}}$.
$\Rightarrow \text{probability=}\dfrac{\text{17}}{\text{19}}$.
∴ The probability that the weight of a student in the class is at most 60 kg is $\dfrac{17}{19}$.

(ii) We have given that the weight of a student in the class is at least 60 kg. This means that the minimum weight of the student should be 36 kg. So, this makes us find the probability that weight of a student in the class should be greater than or equal to 36 kg.
Let us find the total no. of students in the class whose weight is greater than or equal to 36 kg. From the table, we can see that only 9 students are less than 36 kgs.
So, we have $\left( 38-9 \right)=29$ students weighing greater than or equal to 36 kg in the class.
Now, we find the probability that the weight of a student in the class is at least 36 kg.
So, we have $\text{probability=}\dfrac{\text{no}\text{. of students weighing greater than or equal to 36 kg}}{\text{Total no}\text{. of students in the class}}$.
$\Rightarrow \text{probability=}\dfrac{\text{29}}{\text{38}}$.
∴ The probability that the weight of a student in the class is at least 36 kg is $\dfrac{29}{38}$.

(iii) We have given that the weight of a student in the class is not more than 50 kg. This means that the maximum weight of the student should be 50 kg. So, this makes us find the probability that weight of a student in the class should be less than or equal to 50 kg.
Let us find the total no. of students in the class whose weight is less than or equal to 50 kg.
So, we have $\left( 9+5+14+3 \right)=31$ students weighing less than or equal to 50 kg in the class.
Now, we find the probability that the weight of a student in the class is not more than 50 kg.
So, we have $\text{probability=}\dfrac{\text{no}\text{. of students weighing less than or equal to 50 kg}}{\text{Total no}\text{. of students in the class}}$.
$\Rightarrow \text{probability=}\dfrac{\text{31}}{\text{38}}$.
∴ The probability that the weight of a student in the class is not more than 50 kg is $\dfrac{31}{38}$.

Note:
We should not make calculation mistakes while solving this problem. We should not confuse the definitions of at most, at least and not more than a given value. We also need to know that the value of probability lies between 0 and 1 including both. We can also expect this problem by taking the average value of the weight of the students to find the required probability.