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
-----------------------------------------------------------------------------
| please note that only one ques per post can be answered as per HomeworkLib answering guidelines |
1. The amount of soda in a 12 ounce bottle is supposed to be 12 ounces,...
the volumes of soda in a bottle are marketed as 20 ounces but are actually normally distributed with mean 19.8 oz and a standard deviation of 1.2 oz. what is the probability that the volume of soda in a randomly selected bottle will be less than 20 oz?
A soda machine dispenses normally distributed amounts of soda with a mean of 20 ounces and a standard deviation of 0.2 ounce. Are you more likely to randomly select one bottle with more than 21.3 ounces or are you more likely to select a sample of eight bottles with a mean amount of more than 21.3 ounces? Explain.
A machine pours soda into bottles. Suppose experience has shown that the weight of the soda poured is normally distributed and assume that the amount of soda by weight that is poured into each bottle is a normal random variable with a mean of 64 ounces and a standard deviation of 1.5 ounces. What is the probability that the amount of soda that the machine will pour into the next bottle will be more than 65 ounces?
The volumes of soda in quart-sized soda bottles are normally distributed with a mean of 32.3 ounces anda standard deviation of 1.2 ounces. What is the probability that the volume of soda in a randomly selected bottle will be more than 31 ounces?
The contents of soft drink bottles are normally distributed with a mean of twelve ounces and a standard deviation of two ounce. a. What is the probability that a randomly selected bottle will contain more than ten ounces of soft drink? b. What is the probability that a randomly selected bottle will contain between 9.5 and 11 ounces? c. What percentage of the bottles will contain less than 10.5 ounces of soft drink?
The amount of soda a dispensing machine pours into a 12-ounce can of soda follows a normal distribution with a mean of 12.45 ounces and a standard deviation of 0.30 ounce. Each can holds a maximum of 12.75 ounces of soda. Every can that has more than 12.75 ounces of soda poured into it causes a spill and the can must go through a special cleaning process before it can be sold. What is the probability that a randomly selected can will need to...
The amount of soda dispensing machine pours into a can of soda is normally distributed with a mean of 12 ounces and a standard deviation of 0.2 ounces. Find the probability that a can contains less than 11.75 ounces of soda
Soda six-packs Most soda cans list the volume of soda as 12 fluid ounces. As with all process, some variation occurs when filling soda cans. Suppose that a company knows this and tries to over-fill cans a bit, so that the actual volume of soda in a can follows a normal distribution with mean 12.1 fluid ounces and standard deviation .15 fluid ounces. a) What proportion of soda cans filled by this process will contain less than 12 fluid ounces?...
A soft drink company produces bottles of cola that are supposed to contain 10 ounces. When the bottling machine is working correctly, the number of fluid ounces per bottle is in fact normally distributed with mean 10 ounces and standard deviation 0.42 ounces. A customer buys nine bottles of this type of cola. What is the probability that the average volume of cola in the nine bottles is more than 9.7 ounces but less than 10.2 ounces? (A) 0.9074 (B)...
A certain brand of apple juice is supposed to have 64 ounces of juice. The filling machine is not precise, and the exact amount of juice varies from bottle to bottle. Because the penalty for under filling is severe, the quality control manager wishes to verify the mean amount of juice in each bottle. She takes a random sample of 25 bottles, finding a mean of 63.6 ounces and a standard deviation of 0.8 ounces. The data from the 25...