a mean of 3 out 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​

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Answer:

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by the Rishabh

Step-by-step explanation:

mean of 3 out of 5 students

x 3 and 5 product of means product of extreme 3 and 4 is product of means 5 and 8 is the product of extreme x and your answer is coming follow the Rishabh

The probability of less than 4 students asking for tomato sauce along with their meal would be:

0.738

Given that,

Mean of the students asking for tomato sauce = 3/5

No. of random samples collected = 8 students

Given that,

Less than 4 = 0, 1, 2, 3

Let x be the number of students who ask for tomato sauce with their meal.

So,

[tex]P(x < 4) = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3)[/tex]

P(x = o) = [tex]C^{0} _{8} ( 1 - 3/5)^8 = 0.0007[/tex]

P(x = 1) = [tex]C^{1} _{8} ( 3/5) (1 - 3/5)^7 = 0.0079[/tex]

P(x = 2) = [tex]C^{2} _{8} (3/5)^2 ( 1 - 3/5)^6 = 0.0413[/tex]

P(x = 3) = [tex]C^{3} _{8} (3/5)^2 ( 1 - 3/5)^5 = 0.1239[/tex]

Using binomial distribution,

[tex]P(x< 4) = 0.0007 + 0.0079 + 0.0413 + 0.1239[/tex]

[tex]= 0.738[/tex]

Thus, 0.738 is the correct answer.

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