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3 years ago

In how many ways can the letters in the word PAYMENT be arranged if the letters are taken 5 at a time?

2 answers:

4 0

This is a permutation problem in which you are to arrange the objects and the order doesn't matter. You can easily calculate it using your scientific calculator. Just use the formula nPr, where n is the total number of objects taken r at a time.

PAYMENT = 7 letters => 7P5 = 2520
There are 2,520 ways

For butterfly, its quite tricky because there are two letters. Oder does matter here, since no matter which t comes first, that is still the same. So, this is what you do:

BUTTERFLY = 9 letters
9P5 ÷ 2! => since there are two same letters
15120 ÷ 2 = 7560
There are 7560 ways.

LenKa [72]3 years ago

4 0

PAYMENT be arranged letters are taken 5 times then total 35 letters
BUTTERFLY be arranged letters are taken 5 times then total 45 letters

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Answer:

Inferential statistics.

Step-by-step explanation:

We have been given a statement. We are asked to determine whether the given statement describes a descriptive or inferential statistic.

Statement: A survey of 3459 people revealed that 52% work a full-time job; therefore it can be assumed that 52% of the U.S. population works a full-time job.

We know that descriptive statistics represents the description about population using the data through numerical calculations, graphs or tables. While inferential statistics makes predictions about a population based on a sample of data taken from the population.

Since our statement gives the prediction about people, who work full-time in U.S. based on a survey of 3459 U.S. citizens, therefore, the given statement is inferential statistic.

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Step-by-step explanation:

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Based on a survey, assume that 43% of consumers are comfortable having drones deliver their purchases. Suppose we want to find

svlad2 [7]

Answer:

The probability of getting two consumers comfortable with drones is 0.3424.

Step-by-step explanation:

The probability that a consumer is comfortable having drones deliver their purchases is, p = 0.43.

A random sample of n = 5 consumers are selected, and exactly x = 2 of them are comfortable with the drones.

To compute the probability of getting two consumers comfortable with drones followed by three consumers not comfortable, we will use the Binomial distribution instead of the multiplication rule to find the probability.

This is because in this case we need to compute the number of possible combinations of two consumers who are comfortable with drones.

So, X = number of consumers comfortable with drones, follows a Binomial distribution with parameters n = 5 and p = 0.43.

Compute the probability of getting two consumers comfortable with drones as follows:

$P(X=x)={5\choose x}\ 0.43^{x}\ (1-0.43)^{5-x};\ x=0,1,2,3...$

$P(X=2)={5\choose 2}\ 0.43^{2}\ (1-0.43)^{5-2}$

$=10\times 0.1849\times 0.185193\\=0.342421857\\\approx 0.3424$

Thus, the probability of getting two consumers comfortable with drones is 0.3424.

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