Question

# A standard normal random variable is a random variable that is normally distributed with mean equal...

A standard normal random variable is a random variable that is normally distributed with mean equal to 1 and standard deviation equal to 1.

True

False

A standard normal random variable is a random variable that is normally distributed with mean equal to 0 and standard deviation equal to 1

So, the above statement given is FALSE

The normal distribution is a continuous probability distribution. This has several implications for probability.

• The total area under the normal curve is equal to 1.
• The probability that a normal random variable X equals any particular value is 0.
• The probability that X is greater than a equals the area under the normal curve bounded by a and plus infinity (as indicated by the non-shaded area in the figure below).
• The probability that X is less than a equals the area under the normal curve bounded by a and minus infinity (as indicated by the shaded area in the figure below).