Business Statistics Questions on probability?
1.What is the probability that someone will score between 200,000 points and 220,000 points?
2.What is the probability that someone will score between 180,000 points and 220,000 points?
3.What is the probability that someone will score between 220,000 points and 260,000 points?
4.What is the probability that someone will score more than 260,000 points?
5.What is the probability that someone will score less than 220,000 points?
Favorite Answer
Let X ~ Normal(μ = 200000, σ = 40000)
(1)
P(200000 < X < 220000) = P( (200000 - 200000) / 40000 < Z < (220000 - 200000) / 40000) = P(0 < Z < 0.5) = P(Z < 0.5) - P(Z < 0) = 0.6914625 - 0.5000 = 0.1914625 (2) P(180000 < X < 220000) = P(-0.5 < Z < 0.5) = P(Z< 0.5) - P(Z < -0.5) = 0.3829249 (3) P(220000 < X < 260000) = P(0.5 < Z < 1.5) = P(Z < 1.5) - P(Z < 0.5) = 0.2417303 (4) P(X > 260000)
= P(Z > (260000 – 200000) / 40000)
= P(Z > 1.5)
= 1 – P(Z < 1.5) = 0.0668072 (5) P(X < 220000) = P(Z < 0.5) = 0.6914625
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