Solve x/2+ 7=14 record your steps
2 answers:
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Answer:
The proportion of exam scores that are lower than Irina's score is 0.9938
Step-by-step explanation:
<u>Data</u>
- mean: 80 points
- standard deviation (sd): 6 points
- value of interest (x): 95 points
z-score is computed as follows:
z = (x - mean)/sd
z = (95 - 80)/6 = 2.5
We want to find:
P(z < 2.5)
From the table attached:
P(z < 2.5) = 0.9938
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%.