Answer: 3
Step-by-step explanation:
Given : The average time required to complete an accounting test : [tex]\lambda = 55 \text{ minutes}=0.9167\text{ hour}[/tex]
Interval = (45, 60) minutes
In hour : Interval = (0.75, 1)
The cumulative distribution function for exponential function is given by :-
[tex]F(x)=1- e^{-\lambda x}[/tex]
For [tex]\lambda =0.9167\text{ hour}[/tex]
[tex]P(X\leq1)=1- e^{-(0.9167) (1)}=0.6002[/tex]
[tex]P(X\leq0.75)=1- e^{-(0.9167)(0.75)}=0.4972[/tex]
Then ,
[tex]P(0.75<x<1)=P(X\leq1)-P(X\leq0.75)\\\\=0.6002-0.4972=0.103[/tex]
Now, the number of students from a class of 30 should be able to complete the test in between 45 and 60 minutes =
[tex]0.103\times30=3.09\approx3[/tex]
Hence, the number of students should be able to complete the test in between 45 and 60 minutes =3
