Answer:
The probability that x will take on a value between 120 and 125 is 0.14145
Step-by-step explanation:
For uniform distribution between a & b
Mean, xbar = (a + b)/2
Standard deviation, σ = √((b-a)²/12)
For 110 and 150,
Mean, xbar = (150 + 110)/2 = 130
Standard deviation, σ = √((150-110)²/12 = 11.55
To find the probability that x will take on a value between 120 and 125
We need to standardize 120 & 125
z = (x - xbar)/σ = (120 - 130)/11.55 = - 0.87
z = (x - xbar)/σ = (125 - 130)/11.55 = - 0.43
P(120 < x < 125) = P(-0.87 < x < -0.43)
We'll use data from the normal probability table for these probabilities
P(120 < x < 125) = P(-0.87 < x < -0.43) = P(z ≤ -0.43) - P(z ≤ -0.86) = 0.33360 - 0.19215 = 0.14145
Hope this Helps!!!
