Once a large pink ribbon, the sign of the fight against breast cancer, was erected out of pink post-it notes on a billboard. If
the area of therectangular billboard covered by the ribbon was approximately 4200 square feet, and the width of the billboard was approximately 60 feet, what
was the height of this billboard?
was the height of this billboard?
1 answer:
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Answer:
36.32% probability that at least 47 people experience flu symptoms. This is not an unlikely event, so this suggests that flu symptoms are not an adverse reaction to the drug.
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
Estimate the probability that at least 47 people experience flu symptoms.
Using continuity correction, this is , which is 1 subtracted by the pvalue of Z when X = 46.5.
has a 0.6368
1 - 0.6368 = 0.3632
36.32% probability that at least 47 people experience flu symptoms. This is not an unlikely event, so this suggests that flu symptoms are not an adverse reaction to the drug.