Answer:
A. 25.14%
B. 0.99%
C. 100%
D. 86.07%
Step-by-step explanation:
μ = 52, σ = 3
Each problem gives you an x value and asks you to find a probability. First calculate the z score(s), then look up in a table or use a calculator.
z = (x − μ) / σ
A. Find P(x < 50)
z = (50 − 52) / 3
z = -0.67
P(z < -0.67) = 0.2514
B. Find P(x > 59)
z = (59 − 52) / 3
z = 2.33
P(z > 2.33) = 1 − 0.9901 = 0.0099
C. Find P(x > 40)
z = (40 − 52) / 3
z = -4
P(z > -4) = 1 − 0 = 1
D. Find P(48 < x < 57)
z₁ = (48 − 52) / 3
z₁ = -1.33
z₂ = (57 − 52) / 3
z₂ = 1.67
P(-1.33 < z < 1.67) = 0.9525 − 0.0918 = 0.8607
I used a z score table. For more accurate answers, use a calculator.
