will represent this linear model shown in the data table.
Put the values of the x in the all given equations and then check the value of y if the value of y matches the given values in the option
So if we put the value x=1980 in the then
These values are closest to 70.1 whereas other options do not satisfy the condition.
Thus will represent this linear model shown in the data table.
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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.