Comparing means with known standard deviation known

#1
1). The average number of pages for a simple random sample of 20 physics textbooks is 435. The average number of pages for a simple random sample of 25 mathematics textbooks is 404. Assume that all page length for each types of textbooks is normally distributed. The standard deviation of page length for all textbooks is known to be 50. Assume that it's the standard deviation for all mathematics textbooks and for all physics textbooks.

Assuming that on average, mathematics textbooks and physics textbooks have the same number of pages, what is the probability of picking a sample of 20 physics textbooks and of 25 mathematics textbooks and getting a sample mean so much higher for the physics textbooks (p-value, to four places)?


I'm not sure if what I'm doing is correct. Can you let me know if I'm doing anything anything wrong?


standard deviation of physics/ mathematics textbooks: 50
x1 = 435 x2= 404 n1= 20 n2 =25

standard deviation=
square root (sd ^2)/ (n1) + (sd^2)/(n2)
square root ( 50^2)/ (20) + (50^2)/ (25) = 15

z = standard deviation/ x1 - x2
z= 15/ 435-404
= .9803

I'm not sure what to do after this, or even if I approached this problem correctly.
Please Help? :confused: