Question

A bakery opens every day from Monday to Saturday, but only in the morning
on Wednesdays. It is known that the number of bread rolls sold daily follows
a Gaussian distribution with mean 130 and standard deviation 20 with the
exception of Wednesdays for which the distribution of the number of bread
rolls sold is still Gaussian but with mean 100 and standard deviation 30.
(a) What is the probability that on a Wednesday the bakery will sell more
than 140 bread rolls?
(b) What is the probability that on a random opening day the bakery will
sell more than 140 bread rolls?
(c) What is the probability that in a week the bakery will sell more than
800 bread rolls?

Answer 1

x= Wednesday the bakery will sell

l

y=daily sell expect Wednesday

z=x+y=weekly bakery sell

(a) What is the probability that on a Wednesday the bakery will sell more
than 140 bread rolls?

ie P(X>140)

P(X>140)=1-P(X<140)

=1-P(Z<0.5)

=1-0.6914

#value of z is obtain from standard normal table

P(x>140)=0.3085

b) What is the probability that on a random opening day the bakery will
sell more than 140 bread rolls?

ieP(y>140)

Ans:

P(y>140)

P(y>140)=1-P(y<140)

=1-P(Z<1.33)

=1-0.9088

#value of z is obtain from standard normal table

P(Y>140)=0.0912

c) What is the probability that in a week the bakery will sell more than
800 bread rolls?

ie P(Z>800)

Ans: P(Z>800)

P(Z>800)=1-P(Z<800)

=1-P(z<11.14)

=1-1

#value of z is obtain from standard normal table

P(Z>800)=0