Question

Weekly sales of a coffee table at a local store follows a normal distribution with average of 50 and standard deviation of 10.

a. (5 points) What is the probability of a week with sales below 40 tables?

b. (5 points) What is the probability of a week with sales between 40 and 60 tables?

c. (5 points) What is the probability of a week with sales above 60 tables?

d. (5 points) Given that inventories are replenished once a week. If the store wants to ensure enough tables for 95% of the time, how many tables are needed at the beginning of each week?

e. Draw a normal curve using ggplot 2 (hint density plot without the density part)

Answer 1

a)

We have to find the probability of a week with sales below 40 tables

It is given that average=50

Standard deviation=10

using Z table let us find the value

Proabibility  will be= 0.1587

b)

We have to find the probability of a week with sales between 40 and 60

It is given that average=50

Standard deviation=10

using Z table let us find the value

and

Probability will be 0.8413-0.1587=0.6826

c)

What is the probability of a week with sales above 60 tables

It is given that average=50

Standard deviation=10

using Z table let us find the value

probability will be =1-0.8413=0.1587