Question

Suppose that banana prices at supermarkets in a particular large metropolitan area follow a normal distribution with mean µ= 58.6 cents per pound and standard deviation σ= 4.3 cents per pound.

For parts (a) through (c), what is the probability that the price of bananas at a random supermarket will be:

(a) below 55 cents per pound?

(b) above 65 cents per pound?

(c) Between 57 and 62 cents per pound?

(d) Below 57 cents or above 62 cents per pound?

Answer 1

Solution:
Given that,
μ = 58.6, σ=4.3
a) P(X<55)= p{[(x- μ)/σ]<[(55 - 58.6)/4.3]}
=P(z< -0.84)
P(X< 55)=0.2005 ( from Standard Normal table)
b) P(X>65)=1-P(X<=65)
=1- p{[(x- μ)/σ]<=[(65 - 58.6)/4.3]}
= 1- P(z<= 1.49)
=1- 0.9319 ( from Standard Normal table)
=0.0681
c) P(57<X< 62)

= p{[(57 - 58.6)/4.3]<[(X- μ)/σ]<[(62 - 58.6)/4.3]}
=P(-0.37<Z< 0.79)
= p(Z< 0.79) - p(Z< -0.37)

= 0.7852 - 0.3557 ( from. Standard Normal table)
=0.4295
d)P(below 57 or above 62)=1- P(57<X< 62)
= 1-0.4295
=0.5705