A science teacher has 0.4 liter of seawater. She gives each of her 22 students a container and a 5-milliliter spoon. She then as
2 answers:
0.4 liter means 400 ml (milliliter).
We know that 1 spoon is 5 ml. Thus, if each student takes out 2 spoons, then each student will take out 10 ml of water.
There are 22 students, so each student will take out 220 ml.
Thus, the milliliters of seawater that will be left after all 22 students have filled their containers is:
ml
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Answer:
The probability that exactly 27 of 104 eligible voters voted is 0.057 = 5.7%.
Step-by-step explanation:
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 distributions 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 case, assume that 104 eligible voters aged 18-24 are randomly selected.
This means that .
Suppose a previous study showed that among eligible voters aged 18-24, 22% of them voted.
This means that
Mean and standard deviation:
Probability that exactly 27 voted
By continuity continuity, 27 consists of values between 26.5 and 27.5, which means that this probability is the p-value of Z when X = 27.5 subtracted by the p-value of Z when X = 26.5.
X = 27.5
has a p-value of 0.8621
X = 26.5
has a p-value of 0.8051
0.8621 - 0.8051 = 0.057
The probability that exactly 27 of 104 eligible voters voted is 0.057 = 5.7%.