It is known that the length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute. Find the probability that a randomly selected college student will find a parking spot in the library parking lot in less than 3 minutes.
Answers
Step-by-step explanation:
The length of time it takes college students to find a parking spot in the library parking lot follows a normal distribution with a mean of 4.0 minutes and a standard deviation of 1 minute. Find the probability that a randomly selected college student will take between 2.5 and 5.0 minutes to find a parking spot in the library lot.
Answer:
Parameters:
μ
=
3.5
minutes
(Population mean)
σ
=
1
minutes
(Population standard deviation)
P
(
x
>
3
minutes
)
=
?
z
−
score
––––––––––
z
0
=
x
0
−
μ
σ
=
3
−
3.5
1
=
−
0.50
Then
P
(
x
>
3
minutes
)
=
P
(
z
>
−
0.50
)
P
(
x
>
3
minutes
)
=
1
−
P
(
z
<
−
0.50
)
Now, using the cumulative standard normal distribution table:
P
(
z
<
−
0.50
)
is found by reading down the
z
column to the row
−
0.5
and then selecting the probability from
the column labeled
0.00
to be
0.3085
.
Finally
P
(
x
>
3
minutes
)
=
1
−
0.3085
P
(
x
>
3
minutes
)
=
0.6915
P
(
x
>
3
minutes
)
=
69.15
%