Question

A mean of 3 out of 5 students request for tomato sauce with their meal in a canteen. A
random sample of 8 students is selected, what is the probability that less than 4 students
request for tomato sauce with their meal?

Answer 1

Answer:

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Answer 2

The probability that less than 4 students request for tomato sauce with their meal is 0.1736704.

Step-by-step explanation:

Given:

Mean of 3 out of 5 students request for tomato sauce with their meal in a canteen.

A random sample of 8 students is selected.

Less than 4 students request for tomato sauce with their meal.

To Find:

The probability that less than 4 students request for tomato sauce with their meal.

Formula Used:

P(X=k)= nCk             -------------  formula no.01

Here, P(X=k) = The probability of  getting k items out of  number of n items.

           n = number of  students  selected

           X= A  random variable which takes value of k

           k = number  of students request for tomato sauce with their meal

           p = probability of getting  request for tomato sauce with their meal in a canteen.

           q = probability of  getting not getting request for tomato sauce with their meal in a canteen.

Solution:

Let X= the number of students request for tomato sauce with their meal in a canteen.

X∼Bin(n,p).

As given,mean of 3 out of 5 students request for tomato sauce with their meal in a canteen.

Probability $p=\frac{3}{5} =0.6$

$q=1-p =1-0.6 =0.4$

The probability that less than 4 students request for tomato sauce with their meal

$P(X < 4)=P(X=0)+P(X=1)+P(X=2)+P(X=3)$

                $=8_{C} _{0} (0.6)^{0} (0.4)^{8-0} +8_{C} _{1} (0.6)^{1} (0.4)^{8-1}+8_{C} _{2} (0.6)^{2} (0.4)^{8-2}+8_{C} _{3} (0.6)^{3} (0.4)^{8-3}$

$=(\frac{8!}{(8-0)!.0!} ) (0.6)^{0} (0.4)^{8-0} +(\frac{8!}{(8-1)!.1!} ) (0.6)^{1} (0.4)^{8-1}+(\frac{8!}{(8-2)!.2!} )(0.6)^{2} (0.4)^{8-2}+(\frac{8!}{(8-3)!.3!} )(0.6)^{3} (0.4)^{8-3}$

$=0.00065536+0.00786432+0.04128768+0.12386304$

$=0.1736704$

Thus,the probability that less than 4 students request for tomato sauce with their meal is 0.1736704.

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