You scored 48 out of 51 on your recent quiz. What percent did you get correct?
2 answers:
Answer: 94.11%
Step-by-step explanation:
1. You must keep on mind the information given in the problem. You know that the scored 48 out of 51 on your recent quiz.
2. Therefore, to calculate the percent you got correct, you must divide 48 points by 51 points and multiply by 100, as you can see below:
3. Let's call the percent you got correct. Then, you obtain the following result:
%
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Answer:
C. 0.896
Step-by-step explanation:
We use the binomial approximation to the normal 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 probability that at least seventy percent of the sample prefers Coke to Pepsi?
0.7*80 = 56.
This probability is 1 subtracted by the pvalue of Z when X = 56. So
has a pvalue of 0.1040.
1 - 0.1040 = 0.8960
So the correct answer is:
C. 0.896