ITPEC FE Morning April 2022 Question 3

A continuous, bell-shaped distribution symmetric about its mean — the normal distribution is defined by its mean and standard deviation, and most values cluster around the mean.

The normal (Gaussian) distribution is continuous: the variable can take any real value. Its density curve is a bell that peaks at the mean and falls off equally on both sides, so the mean, median and mode coincide. About 68% of values lie within one standard deviation of the mean and about 95% within two.

Answer (b)

Why not others:

• •(a) — the bathtub curve is the failure rate plotted over a product's life: high early failures, a flat random-failure period, then wear-out
• •(c) — counting how many times an event occurs in a fixed interval is the Poisson distribution
• •(d) — a discrete distribution in which every outcome is equally likely, such as a fair die, is the discrete uniform distribution

Key rule: Tell distributions apart by two questions: is the variable continuous or discrete, and what shape does the curve have?

Basic Theory · AI-written, may contain errors