Can someone check my work?

Q

1. A recent study found that, at most, 32% of people who have been in a plane crash have died. In a sample of 100 people who were in a plane crash, 38 died. Is the study statement believable?

:Solution

H(null): P= 0.32

H(alternative): P>0.32 Right tailed

P(hat): 0.38

P= 0.32

n= 100

Then you use the test statistic

z= P(hat)-P/Sqrt(pq/n)

z= 0.38-0.32/sqrt(0.32 x 0.68/100)~ 1.29

So I look for the area on the z score chart and it should be 0.90147. However since that's the area on the left side of the z score. So i must do 1-0.90147= .0985

.0985<0.05 so Reject H(null).....So the statement is believable right?