1. The amount of soda in a 12 ounce bottle is supposed to be 12 ounces, right? There is some variability in the amount that the machines dispense into the bottles. Let the real amount of soda in each bottle follow a Normal distribution with mean 12.2 and standard deviation 0.3.
a. If the bottle can only hold 13 ounces, what is the probability the bottle will overflow? In other words, what is the probability that the machine dispenses more than 13 ounces?
b. If fifteen percent of bottles hold not enough soda to be considered sellable, what is the minimum amount of soda necessary to be sellable? In other words, what is the 15th percentile of soda dispensed?
2. The amount of bottled water Americans consume in each year is estimated to be Normally distributed, with a mean of 32.5 gallons and a standard deviation of 12 gallons.
a. Find the probability that someone consumes more than 35 gallons of bottled water in year.
b. Find the probability that someone consumes between 10 and 25 gallons of bottled water in a year.
c. Ninety-five percent of people consume less than how much bottled water in a year?
d. There’s only a ten percent probability that someone consumes at most how much bottled water in a year?
3. A college only accepts students whose GPA is in the top 15% of all applicants. GPA for applicants is distributed Normal, with mean 3.5 and standard deviation 0.1. Find the GPA necessary to get into this college.
1)
a)
µ = 12.2
σ = 0.3
right tailed
X ≥ 13
Z = (X - µ ) / σ = 2.67
P(X ≥ 13 ) = P(Z ≥
2.67 ) = P ( Z <
-2.67 ) = 0.0038
excel formula for probability from z score is
=NORMSDIST(Z)
the probability that machine dispense more than 13 ounces=0.0038
b)
µ = 12.2
σ = 0.3
percentile = 0.15
Z value at 0.15 =
-1.036 (excel formula =NORMSINV(α))
z=(x-µ)/σ
so, X=zσ+µ= -1.036 *
0.3 + 12.2
X = 11.8891
so, 15th percentile is 11.89 ounces
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