In western Kansas, the summer density of hailstorms is estimated at about 1.4 storms per 5 square miles. In most cases, a hailstorm damages only a relatively small area in a square mile. A crop insurance company has insured a tract of 10 square miles of Kansas wheat land against hail damage. Let r be a random variable that represents the number of hailstorms this summer in the 10-square-mile tract. a) If there already have been two hailstorms this summer, what is the probability that there will be a total of four or more hailstorms in this tract of land? Compute P(r ≥ 4 | r ≥ 2). (Round your answer to four decimal places.) b) If there already have been three hailstorms this summer, what is the probability that there will be a total of fewer than six hailstorms? Compute P(r < 6 | r ≥ 3). (Round your answer to four decimal places.)
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.
In western Kansas, the summer density of hailstorms is estimated at about 1.4 storms per 5 square miles. In most cases, a hailstorm damages only a relatively small area in a square mile. A crop insurance company has insured a tract of 10 square miles of Kansas wheat land against hail damage. Let r be a random variable that represents the number of hailstorms this summer in the 10-square-mile tract.
a) If there already have been two hailstorms this summer, what is the probability that there will be a total of four or more hailstorms in this tract of land? Compute P(r ≥ 4 | r ≥ 2). (Round your answer to four decimal places.)
b) If there already have been three hailstorms this summer, what is the probability that there will be a total of fewer than six hailstorms? Compute P(r < 6 | r ≥ 3). (Round your answer to four decimal places.)
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