Converting one normal distribution to another

Question

I have a long data similar to this; between 15 and 25

consider its mean as m and calculated standard deviation using this formula.

I assumed the above data as a normally distributed data and can calculate Zscore using this formula

I want to convert the X data to an another normal distribution data Y

X                  Y
15              50
15.1578368505   49.928991715
15.4012367562   49.5834109487
15.519892273    49.4143896331
15.6799092721   49.2835022539
15.9227554377   49.2641596452
21.1484143527   3.5582245984
21.3897462389   3.3444121792
21.5833838186   3.3247349532
25              1

here also i have one more condition

From the X series lowest value(ie 15) will point to the highest Y(ie 50) and the highest X series value(25) will point to the lowest of Y series(1) value

eg: if i select X=16 then Y=48.33

What should i do know?

Edited I have tried this

• Calculated Z score of X series
• Used this Z score to find x in the second equation

• The resultant x gave approximate results

     15=0.8567432(approximately to 1)
     25=50.367857(approximately to 50)
  

But I wanted like this

       15=50.367857(approximately to 50)
       25=0.8567432(approximately to 1)

any idea?