Normal distribution

Question code: 167835211

Question 2503

In a supermarket, apples can be bought in bags and oranges can be bought in boxes and are sold by weight. The masses, in kg, of a bag of apples and a box of oranges are modelled as having independent normal distribution with means and standard deviation as shown in the table.
Mean mass Standard deviation
Bag of apples 2.1 0.7
Box of oranges 9.5 2
Apples are sold at $4 per kg and oranges at $2 per kg.

(i)

Find the probability that a randomly chosen bag of apples has a selling price exceeding $8.5
[2]

(ii)

Find the probability that a randomly chosen bag of apples has a selling price exceeding $8.5 and a randomly chosen box of oranges has a selling price exceeding $19.5
[3]

(iii)

Find the probability that the total selling price of a randomly chosen bag of apples and a randomly chosen box of oranges is more than $28
[4]

(iv)

Explain why the answer to part (iii) is greater than the answer to part (ii).
[1]
Answer

(i)

0.486.

(ii)

0.219.

(iii)

0.451.

(iv)

The event in part (ii) is a subset of the event in part (iii).
Question code: 167835211