The table below shows the percentage of households that own a microwave in different countries. Construct a stem-and-leaf plot o
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Answer:
(a) The probability mass function of <em>X</em> is:
(b) The most likely value for <em>X</em> is 1.32.
(c) The probability that at least two of the four selected have earthquake insurance is 0.4015.
Step-by-step explanation:
The random variable <em>X</em> is defined as the number among the four homeowners who have earthquake insurance.
The probability that a homeowner has earthquake insurance is, <em>p</em> = 0.33.
The random sample of homeowners selected is, <em>n</em> = 4.
The event of a homeowner having an earthquake insurance is independent of the other three homeowners.
(a)
All the statements above clearly indicate that the random variable <em>X</em> follows a Binomial distribution with parameters <em>n</em> = 4 and <em>p</em> = 0.33.
The probability mass function of <em>X</em> is:
(b)
The most likely value of a random variable is the expected value.
The expected value of a Binomial random variable is:
Compute the expected value of <em>X</em> as follows:
Thus, the most likely value for <em>X</em> is 1.32.
(c)
Compute the probability that at least two of the four selected have earthquake insurance as follows:
P (X ≥ 2) = 1 - P (X < 2)
= 1 - P (X = 0) - P (X = 1)
Thus, the probability that at least two of the four selected have earthquake insurance is 0.4015.
Irrational numbers are the subset of real numbers that are not at all connected to the rest of numbers.
The subsets of real numbers are natural numbers, whole numbers, integers, rational numbers and irrational numbers.
Natural numbers are subset of whole numbers, which are subset of integers, which are subset of rational numbers. Hence, all of them are interconnected. The set of irrational numbers is the only subset of real numbers which is not associated with the rest.
For example:-
1 is a natural number, whole number, integer, rational number but not irrational number. On the other hand, is an irrational number but none of the rest.
To learn more about real numbers, here:-
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