Answer :
Answer:
a) 0.7063; b) 0.0228; c) 0.2709
Step-by-step explanation:
We use z scores for these problems. The formula for a z sore is
[tex]z=\frac{X-\mu}{\sigma}[/tex]
For part a,
We want P(5 ≤ X ≤ 11):
z = (5-9.6)/2.3 = -4.6/2.3 = -2
z = (11-9.6)/2.3 = 1.4/2.3 = 0.61
The area under the curve to the left of z = -2 is 0.0228. The area under the curve to the left of z = 0.61 is 0.7291. This makes the area between them
0.7291 - 0.0228 = 0.7063
For part b,
We want P(X ≤ 5):
z = (5-9.6)/2.3 = -4.6/2.3 = -2
The area under the curve to the left of z = -2 is 0.0228.
For part c,
We want P(X > 11):
z = (11-9.6)/2.3 = 1.4/2.3 = 0.61
The area under the curve to the left of z = 0.61 is 0.7291. However, we want the area to the right; this means we subtract from 1:
1-0.7291 = 0.2709
