Statistics Questions

#1: Metro Subway Navigation app helps Metro’s 5.8 million daily riders navigate Metro’s complex subway system in real time. Due to construction at Industry Station, a team of Metro Subway App workers are recalculating transfer times between platforms 1D and 2K. The mean transfer time between platforms is 70 seconds with a standard deviation of 12 seconds.

Young Lovers are in no hurry to say goodbye. So they are causally walking from platform 1D to 2K, where one will head east and the other west. How long will it take Young Lovers, keeping a casual pace, to make the transfer?

Input
Mean &
Std Dev
↓
↓↓
↓↓↓
Input X1 & X2
ND PARAMETERS
Mean
μ =
0
Standard Deviation
σ =
1
↓↓↓
AREA btw TWO OBSERVED X-VALUES
x1,smaller value =
x2,larger value =
Probability
z1 = -1.5
=
-1.5
1.5
86.64%
z2 =
AREA OUTSIDE OF TWO OBSERVED X-VALUES
Probability
=
13.36%
Input X1 ↓↓↓
AREA for LEFT-TAIL, ONE OBSERVED X-VALUE
x1 =
2
μ =
σ =
0
1
Probability =
z1 =
Input X2
↓↓↓
AREA for RIGHT-TAIL, ONE OBSERVED X-VALUE
x2 =
2
μ =
σ =
0
1
Probability =
z2 =
CONVERTING A PROBABILITY TO AN OBSERVED VALUE
Proababiity =
0.95
Mean =
0
Z =
Std Deviation =
1
Observed Vaue (X):
SND (μ,σ)
RVED X-VALUES
0.45
0.4
0.35
0.3
0.25
1.50
0.2
OBSERVED X-VALUES
0.15
0.1
0.05
0
-5
-3
-1
1
-0.05
STANDARD DEVIATIONS
SND (μ,σ)
0.45
OBSERVED X-VALUE
0.4
97.72%
0.35
0.3
2.00
0.25
0.2
0.15
0.1
0.05
3
5
0.05
0
-5
-4
-3
-2
-1
-0.05
0
1
2
3
4
5
STANDARD DEVIATIONS
SND (μ,σ)
0.45
E OBSERVED X-VALUE
0.4
2.28%
0.35
0.3
2.00
0.25
0.2
0.15
0.1
0.05
0
-5
-3
-1
-0.05
1
STANDARD DEVIATIONS
3
5
AN OBSERVED VALUE
1.645
Observed Vaue (X):
1.64
5