In the Ardmore Hotel, 20 percent of the guests (the historical percentage) pay by American Express credit card. (a) What is the expected number of guests until the next one pays by American Express credit card? Expected number of guests (b) What is the probability that the first guest to use an American Express is within the first 10 to checkout? (Round your answer to 4 decimal places.) Probability

(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 X 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, p = 0.20.

The random variable X follows a Geometric distribution since it is defined as the number of trials before the first success.

The probability mass function of X 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.

1,407.5 hours

step-by-step explanation:

we first convert all the time to hours and then sum them up.

there are 24 hours in 1 day, in 58 days, there are 24 x 58 = 1,392 hours.

there are 60 minutes in 1 hour, thus, 30 minutes will be equivalent to 30 / 60 = 0.5 hours.

therefore, the number of hours it will take mercury to complete a full rotation is 1,392 + 15 + 0.5 = 1,407.5 hours

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step-by-step explanation:

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