The answer is ? Because im trying to find out
1 answer:
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Answer:
c. 0.16
Step-by-step explanation:
For each passenger there are only two possible outcomes. Either they are caught with a gun, or they are not. The probability of a passenger being caught with a gun is independent from other passengers. So we use the binomial probability distribution to solve this question.
However, we are working with samples that are considerably big. So i am going to aproximate this binomial distribution to the normal.
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 tomorrow more than 35 domestic passengers will accidentally get caught with a gun at the airport?
This probability is 1 subtracted by the pvalue of Z when X = 35. So
has a pvalue of 0.8186
1 - 0.8186 = 0.1814.
The closest answer is:
c. 0.16
The 0.8% of the production is defective if a quality control process finds 77.6 defects for every 9,700 units of production.
<h3>What is the percentage?</h3>It is defined as the ratio of two numbers expressed in the fraction of 100 parts. It is the measure to compare two data, the % sign is used to express the percentage.
We have:
A quality control process finds 77.6 defects for every 9,700 units of production.
The percent of the production is defective:
= 0.8 %
Thus, the 0.8% of the production is defective if a quality control process finds 77.6 defects for every 9,700 units of production.
Learn more about the percentage here:
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