Question

Below is a cumulative relative frequency graph for the lengths, in minutes, of 200 songs

Answer 1

Answer:

Adding 5 seconds would give

Mean= X`= 258.8 seconds

Standard Deviation=S=   82.8 seconds

The standard deviation remains the same.

Mean z= 0

Standard Deviation z= 1

Step-by-step explanation:

Mean= 4.23 minutes,

Standard Deviation=  1.38 minutes

He wants to add 5 seconds of silence between songs,

So we will convert these minutes into seconds

Mean= 4.23 minutes * 60= 253.8 seconds

Standard Deviation=  1.38 minutes* 60= 82.8 seconds

Adding 5 seconds would give

Mean= X`= 4.23 minutes * 60 +5 = 258.8 seconds

Standard Deviation=S=  1.38 minutes* 60= 82.8 seconds

The standard deviation remains the same.

b. Transforming into z- scores would give

Mean z= x`-u/s= 4.23-4.23/1.38= 0

Standard Deviation z= s/s= 1.38/1.38= 1

This is because changing into z- scores is simply a linear transformation.