How many gallons of a 70% antifreeze solution must be mixed with 90 gallons of 20% antifreeze to get a mixture that is 60% antif
1 answer:
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Answer:
Part 1) 10 modules per floor
Part 2) Two different rectangular prism
Step-by-step explanation:
Part 1)
Let
x ----> the number of modules
y ---> the number of stories
we have
Divide the number of modules by the number of stories
so
Part 2) How many different rectangular prisms could be made from that number?
The number is 10
Look at the factors of 10
They are 1,2 ,4,5 and 10
Pick any two of these factors and determine if there is a third value from this list so that the product of the three factors is 10
There are 2 combinations that will work :
1 0×1×1
2 ×5×1
Answer:
10.93% probability of observing 51 or fewer vapers in a random sample of 300
Step-by-step explanation:
I am going to use the normal approximation to the binomial to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
The standard deviation of the binomial distribution is:
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean and standard deviation
, the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that ,
.
In this problem, we have that:
So
What is the approximate probability of observing 51 or fewer vapers in a random sample of 300?
Using continuity corrections, this is , which is the pvalue of Z when X = 51.5 So
has a pvalue of 0.1093.
10.93% probability of observing 51 or fewer vapers in a random sample of 300