How much of a 60% acid solution must be mixed with 50 gallons of a 24% acid solution to obtain a solution that is 50% acid?
2 answers:
X gallons of a 60% acid solution contains 60%×x=0.6x gallons of acid.
50 gallons of a 24% acid solution contains 24%×50=0.24×50=12 gallons of acid.
After mixing, there will be x+50 gallons of a solution, and 0.6x+12 gallons of acid. The concentration must be 50%, so the volume of acid divided by the volume of the solution is 50%, or 0.5.
The answer is A. 130 gallons.
50 gallons of a 24% acid solution contains 24%×50=0.24×50=12 gallons of acid.
After mixing, there will be x+50 gallons of a solution, and 0.6x+12 gallons of acid. The concentration must be 50%, so the volume of acid divided by the volume of the solution is 50%, or 0.5.
The answer is A. 130 gallons.
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Answer:
0.8389 = 83.89% probability that the sample mean would be less than 133.5 liters.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the z-score of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
The mean per capita consumption of milk per year is 131 liters with a variance of 841.
This means that
Sample of 132 people
This means that
What is the probability that the sample mean would be less than 133.5 liters?
This is the p-value of Z when X = 133.5. So
By the Central Limit Theorem
has a p-value of 0.8389
0.8389 = 83.89% probability that the sample mean would be less than 133.5 liters.