STAT 410
Practice Problems for 3.4 and 3.5
Spring 2008
1.
A gas station sells three grades of gasoline: regular unleaded, extra unleaded, and
super unleaded. These are priced at $1.55, $1.70, and $1.85 per gallon, respectively.
Let X
1
, X
2
, and X
3
denote the amounts of these grades purchased (gallons) on a
particular day. Suppose the X
i
’s are independent with
μ
1
= 1,000,
μ
2
= 500,
μ
3
= 300,
σ
1
= 100,
σ
2
= 80, and
σ
3
= 50. If the X
i
’s are normally distributed,
what is the probability that revenue exceeds …
a)
$2,600?
b)
$3,000?
2.
Suppose that the actual weight of "10pound" sacks of potatoes varies from sack
to sack and that the actual weight may be considered a random variable having a
normal distribution with the mean of 10.2 pounds and the standard deviation of
0.6 pounds. Similarly, the actual weight of "3pound" bags of apples varies from
bag to bag and that the actual weight may be considered a random variable having
a normal distribution with the mean of 3.15 pounds and the standard deviation of
0.3 pounds. A boyscout troop is planning a camping trip. If the boyscouts buy
3
"10pound" sacks of potatoes and
4
"3pound" bags of apples selecting them at
random, what is the probability that the total weight would exceed 42 pounds?
3.
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 Spring '08
 Monrad
 Normal Distribution, $3,000, $1.70, $1.85, $1.55, $2,955

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