Is this circuit diagram correct?

Looks OK to me, too. Depending on which electret mic you are using, it's possible you may need to use a different resistance value for R1; but other than that it should work.

 

1) The Jfet in an electret mic draws 0.5mA so the value of R1should be reduced to about 10k to prevent the Jfet from saturating.
2) The transistor has a high input impedance then the high 10μF value of C1 passes low earthquake frequencies so its value should be reduced to about 0.22μF and it should be a non-polarized film type.
3) The 2N3904 has an hFE of about 200 so the value of R2 should be increased to about 1M or 1.5M ohms.
4) The low value of the volume control is killing the signal level from the preamp so it should be increased to about 100k ohms.
5) The high 0.1uF value of C3 is killing all medium and high audio frequencies. Remove C3.

Hey, the transistor has a voltage gain of only 10 so it is not needed and a 10μF capacitor can be connected between pin 1 and pin 8 of the LM386 to give it 10 times more gain.