Mathematics: In a hostel, 80 students have food enough for 45 days. How many students should leave the hostel so that the food is enough for 60 days?

In a hostel, 80 students have food enough for

Ответ:

chantianabess36

13.02.2022

Mathematics

a) 10 weeks

b) P(k≤2)=0.190

c) P(k>17)=0.167

Step-by-step explanation:

This problem can be solved applying the geometric distribution.

The probability of needing k weeks to find an acceptable apartment can be written as:

$P(k)=(1-p)^{k-1}p=0.9^{k-1}\cdot 0.1$

a) The expected value of this distribution is:

E(x)=1/p=1/0.1=10

10 weeks

b) The probability of finding an acceptable department in the first 2 weeks is:

$P(k\leq2)=P(1)+P(2)=0.1*0.9^0+0.1*0.9^1\\\\P(k\leq 2)=0.1+0.09=0.19$

c) We have to calculate P(k>17)

$P(k17)=1-\sum_1^{17}P(k_i)\\\\P(k17)=1-(P(1)+P(2)+P(3)+...+P(17))\\\\P(k17)=1-(0.1+0.09+0.081+0.073+0.066+0.059+0.053+0.048+0.043+0.039+0.035+0.031+0.028+0.025+0.023+0.021+0.019)\\\\P(k17)=1-0.833=0.167$

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In a hostel, 80 students have food enough for 45 days. How many students should leave the hostel so that the food is enough for 60 days?

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