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Answer:
(a) The expected number of guests until the next one pays by American Express credit card is 4.
(b) The probability that the first guest to use an American Express is within the first 10 to checkout is 0.0215.
Step-by-step explanation:
The random variable <em>X</em> can be defined as the number of guests until the next one pays by American Express credit card
The probability that a guest paying by American Express credit card is, <em>p</em> = 0.20.
The random variable <em>X</em> follows a Geometric distribution since it is defined as the number of trials before the first success.
The probability mass function of <em>X</em> is:
(a)
The expected value of a Geometric distribution is:
Compute the expected number of guests until the next one pays by American Express credit card as follows:
Thus, the expected number of guests until the next one pays by American Express credit card is 4.
(b)
Compute the probability that the first guest to use an American Express is within the first 10 to checkout as follows:
Thus, the probability that the first guest to use an American Express is within the first 10 to checkout is 0.0215.
The expression (2/7)x (1.4x² - 3.5y) can be written in the form of a polynomial as 0.4x³ - xy.
<h3>What is polynomial?</h3>Polynomial is an algebraic expression that consists of variables and coefficients. Variables are called unknown. We can apply arithmetic operations such as addition, subtraction, etc. But not divisible by variable.
The expression is given below
The expression can be written in the form of the polynomial
The expression in the form of a polynomial is given as
More about the polynomial link is given below.
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