# statistics – Finding a constant using the table of normal distibution

Given $$Xsim N(mu,36)$$, a random sample of $$50$$ of $$X$$ has mean $$20.2$$. Find $$L$$ if $$P(bar{X}

I first tried to normalize it so I could use the $$z$$ score value from the table:

$$Pleft(Z

The equivalent $$z$$ to probability of $$0.95$$ is $$1.64$$. Then

$$z=1.94=frac{L-20.2}{frac{3}{50}},:L=21.02$$

Which is not far off the answer, but something is wrong. Can someone help me find that out?