Exam 17: Continuous Random Variables

The scores on an examination are normally distributed with μ = 75 and σ = 10.What percentage of the scores are between 70 and 90?

If Z has a standard normal distribution,state the mean and standard deviation of Z.

If X is normally distributed with mean μ and standard deviation σ,then what is the approximate probability that μ - 2σ ≤ X ≤ μ + 2σ?

Suppose the cumulative distribution function for the random variable X is given by F(x)= Find P(2 < X < 3).

If Z has a standard normal random variable and P(Z > )= 0.9938,

Suppose X is normally distributed with mean 100 and standard deviation 20.Without using tables,determine the approximate value of P(80 < X < 100).

If Z has a standard normal distribution,find P(Z > 2σ).

The random variable X has density function f(x)= Find (a)P(20 ≤ X ≤ 40)and (b)P(X ≥ 40).