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Probability and Statistical Analysis of Normal Distributions

An assignment covering probability, normal distributions, and statistical analysis.

Amelia Davis
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Probability and Statistical Analysis of Normal Distributions1.Find the following probability for the standard normal random variable zP(-2.5≤z≤2.5)=0.98762. Suppose x is a normal distributed random variable with μ = 15 and= 2. Find each ofthefollowing probabilities.a. P(x≥18.5)=0.0401b. P(x≤11)=0.0228c. P(16.56≤x≤19.58)=0.2067d. P(9.52≤x≤18.6)=0.96103. The ages of a group of 50 women are approximately normally distributed with a mean of 50years and a standard deviation of 5 years. One woman is randomly selected from the group, andher age is observed.a. Find the probability that her age will fall between 55 and 60 years.0.1359b. Find the probability that her age will fall between 49 and 53 years.0.3050c. Findthe probability that her age will be less than 34 years.0.0007d. Find the probability that her age will exceed 41 years0.96414.Financial analysts who make forecasts of stock prices are categorized as either “buy-side”analysts or “sell-side” analysts. The mean and standard deviation of the forecast errors for bothtypes of analysts are shown is the table to the right. Assume that the distribution of forecasterrors are approximately normally distributed.Buy-side analystsSell-side analystsMean.82-.03Standard deviation1.94.86a. Find the probability that a buy-side analyst has a forecast error of + 2.02 or higher0.2681b. Find the probability that a sell-side analyst has a forecast error of + 2.02or higher0.00004. The mean gas mileage for a hybrid car is 56 miles per gallon. Suppose that the gasolinemileage is approximately normally distributed with a standard deviation of 3.2 miles per gallon.

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Statistics

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