Question

Question 7

A retail outlet finds from historic data that it sells an average of 220 copies of a newspaper daily; this figure comes with a standard deviation of 35 units. The sales figures can be approximated to a normal distribution.

1. If the retail outlet wishes to cater to 98% of possible daily demand, how many copies should it stock?

2. If it wishes to cater to 45% of the possible daily demand, how many copies should it stock?

Answer 1

.(a)Mean Demand=220

Standard Deviation of Demand=35

If it wishes to cater to 98% of possible demand,

Cumulative Area  under the Standard Normal Table  from -3 to N(d)=0.98

For N(d)=0.9798, D=2.05

For N(d)=0.9821, D=2.10

By Interpolation,

For N(d)=0.98,

D=2.05+((2.10-2.05)/(0.9821-0.9798))*(0.9800-0.9798)

D=2.05+0.004348=2.054348

Assume,Number of Copies it should stock =X

((X-Mean)/(Standard Deviation ))=2.054348

((X-220)/35)=2.054348

X-220=2.054348*35=71.90218

X=220+71.90218=291.9022

Rounded to nearest whole no.

X=292

Number of copies to be stocked =292

b.If it satisfies 45% of daily demand :

N(d)=0.45

For N(d)=0.45,

Cumulative Area  under the Standard Normal Table \

N(d)=0.4483, D=-0.13

N(d)=0.4522, D=-0.12

By interpolation,

For N(d)=0.45,

D=-0.1236

Assume no. of copies to be stocked =X

((X-220)/35)=-0.1236

X-220=-0.1236*35=-4.326

X=220-4.326=215.67

Rounded to nearest whole Number

X=216

Number of copies to be stocked =216