MATH 134 – Calculus With Fundamentals 2 Discussion – Normal Probabilities using Tabulated Values April 10, 2018

Background

Probabilities for a standard normal random variable (i.e. normal distribution with μ = 0, σ = 1) are given in the table on the back of this sheet.

Important Fact: If Y is normal with mean μ and standard deviation σ, then

Z = \frac{Y − μ}{σ}

is standard normal, and the table can be applied to Z. In today’s discussion, you will practice using the table to answer questions about normally distributed quantities.

Discussion Questions

A) Approximate the area given by

∫_{0}^{1} \frac{1}{\sqrt{2π}} e^{−x^{2}/2} dx

using a Riemann sum with N = 5. How close is your value to the table value .3413? What would you need to do to get a more accurate value?

B) Let Z be a standard normal.

1) Find P (−2.13 < Z < −0.56)

2) Find c such that P (Z > c) = .05

C) Y is normally distributed with mean μ6 and σ = 2. Find

1) P (6 < Y < 7)

2) P (7 < Y < 8)

D) SlimMints (yum!) are sold in two-packs with a stated label weight of 20.4 grams. The actual weights of the packages are normally distributed with mean μ = 21.37 and variance σ^{2} = .16. Let Y be the weight of a single package selected at random from the production line. What is the probability P (Y > 22.07)?

Assignment

Group writeups due at end of class.