Questions from Calculus

Q: Make a small probability table for a discrete random variable X and

Make a small probability table for a discrete random variable X and use it to define E(X ), Var (X ), and the standard deviation of X.

Q: Suppose that the police force in Exercise 23 maintains the same height

Suppose that the police force in Exercise 23 maintains the same height requirements for women as men and that the heights of women in the city are normally distributed, with µ = 65 inches and σ = 1.6...

Q: Explain how to create a probability density histogram.

Explain how to create a probability density histogram.

Q: A medical laboratory tests many blood samples for a certain disease that

A medical laboratory tests many blood samples for a certain disease that occurs in about 5% of the samples. The lab collects samples from 10 persons and mixes together some blood from each sample. If...

Q: Let Z be a standard normal random variable. Find the number

Let Z be a standard normal random variable. Find the number a such that Pr (a ≤ Z ) = .40.

Q: Scores on an entrance exam Scores on a school’s entrance exam are

Scores on an entrance exam Scores on a school’s entrance exam are normally distributed, with µ = 500 and σ = 100. If the school wishes to admit only the students in the top 40%, what should be the cut...

Q: It is useful in some applications to know that about 68%

It is useful in some applications to know that about 68% of the area under the standard normal curve lies between -1 and 1. (a) Verify this statement. (b) Let X be a normal random variable with expect...

Q: (a) Show that about 95% of the area under

(a) Show that about 95% of the area under the standard normal curve lies between -2 and 2. (b) Let X be a normal random variable with expected value µ and variance σ2. Compute Pr (µ - 2σ ≤ X ≤ µ + 2σ)...

Q: The Chebyshev inequality says that for any random variable X with expected

The Chebyshev inequality says that for any random variable X with expected value m and standard deviation σ, Pr (µ - nσ ≤ X ≤ µ + nσ) ≥ 1 -1/n2. (a) Take n = 2. Apply the Chebyshev inequality to an ex...

Q: Do the same as in Exercise 29 with a normal random variable

Do the same as in Exercise 29 with a normal random variable. Exercise 29: The Chebyshev inequality says that for any random variable X with expected value m and standard deviation σ, Pr (µ - nσ ≤ X ≤...