In: Statistics and Probability
At the beginning of the semester, the amount of time a student waits in line at the campus cafeteria is normally distributed with a mean of five minutes and a standard deviation of 1.5 minutes.
If you randomly select 81 students, what is the probability that they have a mean waiting time between 4.7 and 5.8 minutes?
Group of answer choices
.9641
.718
.0359
.282
Solution :
Given that ,
mean =
= 5
standard deviation =
= 1.5
n = 81
= 5
=
/
n= 1.5 /
81=0.1667
P(4.7< <5.8
) = P[(4.7-5) /0.1667 < (
-
) /
< (5.8-5) / 0.1667 )]
= P(-1.80 < Z < 4.79)
= P(Z <4.79 ) - P(Z < -1.80)
Using z table
=1-0.0359
=0.9641
probability=0.9641