Question

Hi, can you help me answer this question, please, thank you:)

Answer 1

Remember that the total probability of an event (the check out) is equal to 1. In our problem, the time it takes to check out is distributed in an interval of 14-1=13min.

a) Therefore, the height of the distribution is given by:

`\begin{gathered} h\cdot13=1 \\ \Rightarrow h=(1)/(13)=0.0769\ldots \\ \Rightarrow h\approx0.0769 \end{gathered}`

Once we have rounded the result, the answer is height=0.0769.

b) Notice that 7min-4min=3min, and the probability is equally distributed along 13 minutes, then:

The answer is P(X<10)=0.6923d) Notice that
`\begin{gathered} P(X<10)+P(X\ge10)=1 \\ \Rightarrow P(X\ge10)=1-P(X<10) \\ \Rightarrow P(X\ge10)=1-(9)/(13)=(4)/(13)=0.307692\ldots \\ \Rightarrow P(X\ge10)\approx0.3077 \end{gathered}`The answer is P(X=>10)=0.3077