The employees of a firm that manufactures insulation are being tested for indications of asbestos in their lungs. The firm is re
quested to send 4 employees who have positive indications of asbestos on to a medical center for further testing. If 55% of the employees have positive indications of asbestos in their lungs, find the probability that 11 employees must be tested in order to find 4 positives. If each test costs 300 Swedish kronor, find the expected value of the total cost of conducting the tests necessary to locate the 4 positives. Swedish kronor Find the variance of the total cost necessary to locate the 4 positives.
1 answer:
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Answer:
b) 6.68%
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
The mean score on the scale is 50. The distribution has a standard deviation of 10.
This means that
Matthew scores a 65. What percentage of people could be expected to score the same as Matthew or higher on this scale?
The proportion is 1 subtracted by the p-value of Z when X = 65. So
has a p-value of 0.9332.
1 - 0.9332 = 0.0668
0.0668*100% = 6.68%
So the correct answer is given by option b.