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AJACW22
Suppose x is a normally distributed random variable with μ = 14 and σ =2. Find each of the following probabilities. a. P (x ≥ 14.5) b. P (x ≤ 11) c. P (14.42 ≤ x ≤ 19.46) d. P (9.12 ≤ x ≤ 16.77)
a. P(x ≥14.5) = 1-P(x≤14.5) =1-P(z≤(14.5-14)/2) =1-P(z≤0.25) =1-0.59871 (using normal table) = 0.50129 I'll try to do the others next.
b. P(x≤11) = P(z≤(11-14)/2) =P(z≤-1.5) =1- 0.93319 (-ve so do 1 minus) = 0.06671
c. Split into P(x ≥14.42) - P(x ≤19.46) =P(z ≥ (14.42-14)/2) - P(z ≤ (19.46-1)/2) =P(z ≥ 0.21) - P(z ≤ 2.73) =0.58317 + 0.99683 - =0.58
d. P(x ≥ 9.12) - P(x ≤ 16.77) =P(z ≥ -2.44) - P(z ≤ 1.385) =0.99266 + 0.91774 - 1 =0.07492
actually that last line should be 0.9104
Thank you. I have another one with different numbers. Sorry I didnt get a chance to solve the first one.