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timofeeve [1]
3 years ago
5

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
Mathematics
1 answer:
xxMikexx [17]3 years ago
3 0

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:

P(X=x)=(1-p)^{x}p;\ x=0,1,2,3...,\ 0

(a)

The expected value of a Geometric distribution is:

E(X)=\frac{1-p}{p}

Compute the expected number of guests until the next one pays by American Express credit card as follows:

E(X)=\frac{1-p}{p}

         =\frac{1-0.20}{0.20}

         =4

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:

P(X=10)=(1-0.20)^{10}\times0.20

                 =0.1073741824\times 0.20\\=0.02147483648\\\approx0.0215

Thus, the probability that the first guest to use an American Express is within the first 10 to checkout is 0.0215.

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The mean height of plants is 44.07cm.

Given that a raj measures the height of 70 plants which is shown in the table in the image attached below.

The mean is defined as the mean value equal to the ratio of the total number of a given set of values ​​to the total number of values ​​contained in that set.

Firstly, we will find the midpoint of the height by using the formula

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When h is 10<h<20 then the midpoint is

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Now, we will find the mean height by using the formula

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Substitute these values in the formula, we get

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Hence,  the estimate of the mean height of the plants when raj measures the height of 70 plants is 44.07cm.

Learn more about mean from here brainly.com/question/3491195

#SPJ4

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