Business Statistics Questions on probability?

The scores on a pinball machine located in the Student Center are normally distributed with a mean of 200,000 points and a standard deviation of 40,000 points.

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?

Top 1 Answers

A few days ago

Merlyn

Favorite Answer

for any normal random variable you can translate into standard units and use the standard normal cdf tables to get the solutions.

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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Business Statistics Questions on probability?

Business Statistics Questions on probability?

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