Given $Xsim N(mu,36)$, a random sample of $50$ of $X$ has mean $20.2$. Find $L$ if $P(bar{X}<L)=0.95$
I first tried to normalize it so I could use the $z$ score value from the table:
$$Pleft(Z<frac{L-mean}{sd}right)=Pleft(Z<frac{L-20.2}{frac{3}{25}}right)$$
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?
