Tutorial 05 Questions 1 2015

ETX1100/ETF5900

Tutorial 5

The normal distribution SOLUTIONS
Part A
A5.1. Instructions for the use of the normal distribution functions NORM.S.DIST,
NORM.S.INV, NORM.DIST, and NORM.INV are provided in section E4.4 of the Excel notes in the Software Information Folder under Week 0 on
Moodle.

(a) Use the Excel function NORM.S.DIST to calculate the following probabilities to four decimal places, where the random variable Z follows a standard normal distribution. Write your answers to four decimal places on this sheet and remember to draw the curves?

For every second question, please use your tables to find the probability as well as Excel.

(i)

P(Z  0.443) 

(ii)

P(Z <1.522) =

(iii)

P(Z  1.944) 

(iv)

P(0  Z  1.282) 

(v)

(vi)

P(1.522 < Z <1.958) =

P(-1  Z  1.282) =

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ETX1100/ETF5900

Tutorial 5

Now we begin with a given probability and have to work backwards to find the corresponding z value.
(b) Use the Excel function NORM.S.INV, and draw curves, to find the value z* for which
(i)

P( Z  z* )  0.5

(ii)

P( Z  z* )  0.895

(iii)

P( Z  z* )  0.054

(iv)

P( Z  z* )  0.025

(v)

P(0  Z  z* )  0.400

(vi)

P( z*  Z  z* )  0.882

(c)
Let X be a normally distributed random variable with mean 10 and standard deviation 4.5.
(i)

(ii)

Use the Excel function NORM.DIST to find P( X  0) .

Use the Excel function NORM.INV to find the value of x* such that

P( X  x* )  0.10 .
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ETX1100/ETF5900

Tutorial 5

A5.2 Suppose Z has a normal distribution with mean 0 and standard deviation 1.
Use a diagram in working out the following.
(a) Use NORM.S.DIST to find the area of the upper tail cut off by 2.327 in the standard normal distribution.

(b) Use NORM.S.INV to find the value of z0.002 , i.e. the z value that cuts off an upper tail of area 0.002.

(c) Use NORM.S.INV to find the two values of z that cut off two tails of total area
0.002.

Part B
B5.3.

When using tables to obtain standard normal probabilities, values of Z can only be