Question

X is a normally distributed variable with mean μ = 17 and standard deviation σ = 3 find:

a) P(x >21)
b) P(x < 15)
c) P(16 < x < 25)

Answer 1

a)0.09176

b)0.22065

c)0.62551

Explanation:

a) p(x>21) = p(z> (21-17)/3)=p(z>1.333) = 1-.90824= 0.09176 (subtracting from one because we are looking at the right side of the graph from the Z-table)

b)p(x<15) = p(z< (15-17)/3)=p(z<-.6667) = 0.22065

c)p(16 < x < 25)= (z(16-17)/3 < p < z(25-17)/3)= z(-.333) < p < z(2.667)=.99621 -.37070 = 0.62551