Each of 12 refrigerators of a certain type has beenreturned to a distributor because of an audible, highpitched,oscillating noise when the refrigerators are running.Suppose that 7 of these refrigerators have a defectivecompressor and the other 5 have less serious problems.If the refrigerators are examined in random order,let X be the number among the first 6 examined that havea defective compressor.a. Calculate P(X 5 4) and P(X # 4)b. Determine the probability that X exceeds its meanvalue by more than 1 standard deviation.c. Consider a large shipment of 400 refrigerators, ofwhich 40 have defective compressors. If X is thenumber among 15 randomly selected refrigeratorsthat have defective compressors, describe a lesstedious way to calculate (at least approximately)P(X # 5) than to use the hypergeometric pmf.
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Each of 12 refrigerators of a certain type has been
returned to a distributor because of an audible, highpitched,
oscillating noise when the refrigerators are running.
Suppose that 7 of these refrigerators have a defective
compressor and the other 5 have less serious problems.
If the refrigerators are examined in random order,
let X be the number among the first 6 examined that have
a defective compressor.
a. Calculate P(X 5 4) and P(X # 4)
b. Determine the
value by more than 1 standard deviation.
c. Consider a large shipment of 400 refrigerators, of
which 40 have defective compressors. If X is the
number among 15 randomly selected refrigerators
that have defective compressors, describe a less
tedious way to calculate (at least approximately)
P(X # 5) than to use the hypergeometric pmf.
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