Question

1. Find the area under the curve and estimates for the mean of 200 with standard deviation 30. Find the following and draw the required area.

1. P(x<155)
2. P(x<228)
3. Between P(155<x<228)
4. Px≥228

Answer 1

Answer a) 0.0668

Step 1: Sketch the curve. The probability that X < 155 is equal to the blue area under the curve. 0.016 0.014 0.012 0.010 0.008 y 0.006 0.004 0.002 0.000 155 -0.002 100 120 140 160 180 200 220 240 260 280 300 х Step 2: Since u = 200 and o = 30 we have: X- P(X< 155 )=P(X - < 155 – 200) P 155 – 200 30 Since Z and 155-200 30 = -1.5 we have: P (X<155)=P(Z<-1.5) Step 3: Use the standard normal table to conclude that: P(Z < -1.5) = 0.0668

Answer b) 0.8238

Step 1: Sketch the curve. The probability that X<228 is equal to the blue area under the curve. 0.016 0.014 0.012 0.010 0.008 у 0.006 0.004 0.002 0.000 228 -0.002 100 120 140 160 180 200 220 240 260 280 300 X Step 2: Since 200 and o=30 we have P(X<228 )=P(X - # <228 – 200 ) =P 228 - 200 30 Since : Z and 228-200 30 0.93 we have: P(X<228) - P(Z < 0.93) Step 3: Use the standard normal table to conclude that: P(Z <0.93) = 0.8238

Answer c) 0.7570

P(155<x<228) = P(x<228) - P(x<155) = 0.8238 - 0.0668

P(155<x<228) = 0.7570

Answer d) 0.1762

P(x≥228) = 1 - P(x<228) = 1 - 0.8238

P(x≥228) = 0.1762