Normal Distribution

Let X∼N(3,2^2). What does this tell us about the distribution of X ?

• X is a binomial with n=3 and p=2

• X is a normal with mean 3 and variance 4

• X is a normal with mean 3 and variance 2

• X is a binomial with mean 3 and variance 2

X is a random normal variable, with mean μ and variance σ. The “standardised form” of X is Z=(X−μ)/σ. What are the mean and variance, respectively, of Z?

• 0,1

• 2,1

• 1,0

• 2,0

Let X~N(5,3^2). Which of the following is a standard normal variable ?

• Z = (X-5) / 5

• Z = (X-3) / 5

• Z = (X-5) / 3

Suppose X∼N(5,3^2). What is P(X≤8) in terms of the standard normal variable Z?

• P(Z≤1)

• P(Z≤ -1)

• P(Z≤0.6)

• P(Z≤1.67)

Suppose X is normally distributed with mean 5. If P(X≤3)=0.2 What is the standard deviation of X?

• σ=−0.4

• σ=−0.42

• σ=0.38

• σ=2.38

X and Y are independent random variables. The mean and variance of X are 2 and 1 respectively. The mean and variance of Y are 3 and 2 respectively.

Which of the statements below about the random variable X−Y is true ?

• X−Y has a mean of 5 and variance 3

• X−Y~ N(-1,1)

• X−Y~ N(-1,3)

• X−Y has a mean of -1 and variance 3