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2 years ago

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A signal can be sent from one location to another by running different colored flags up a flagpole, one above the other. There a

re 15 different colored flags to choose from but only 8 flags will be flown. Find the number of different signals consisting of 8, if the first flag must be blue.
If the first flag is blue then the number of different signals consisting of 8 flags is ??

1 answer:

Verdich [7]2 years ago

8 0

Using the permutation formula, it is found that there are 17,297,280 different signals consisting of 8 flags.

In this problem, the order in which the flags are visited is important, hence the <em>permutation formula</em> is used to solve this question.

<h3>What is the permutation formula?</h3>

The number of possible permutations of x elements from a set of n elements is given by:

$P_{(n,x)} = \frac{n!}{(n-x)!}$

The first flag is blue, then the remaining 7 are taken from a set of 14, hence:

$P_{(14,7)} = \frac{14!}{7!} = 17,297,280$

There are 17,297,280 different signals consisting of 8 flags.

More can be learned about the permutation formula at brainly.com/question/25925367

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Answer:

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(b) 5% of people has an IQ score less than 74 or greater than 126.

(c) 0.15% of people has an IQ score greater than 139.

Step-by-step explanation:

Given information:Scores of an IQ test have a bell-shaped distribution,

mean = 100

standard deviation = 13

According to the empirical rule

68% data lies between $\overline{x}-\sigma$ and $\overline{x}+\sigma$ .

95% data lies between $\overline{x}-2\sigma$ and $\overline{x}+2\sigma$ .

99.7% data lies between $\overline{x}-3\sigma$ and $\overline{x}+3\sigma$ .

(a)

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$\overline{x}+\sigma=100+13=113$

$[\overline{x}-\sigma,\overline{x}+\sigma]=[87,113]$

Using empirical rule we can say that 68% of people has an IQ score between 87 and 113.

(b)

$\overline{x}-2\sigma=100-2(13)=74$

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$[\overline{x}-2\sigma,\overline{x}+2\sigma]=[74,126]$

Using empirical rule we can say that 95% of people has an IQ score between 74 and 126.

The percentage of people has an IQ score less than 74 or greater than 126 is

P = 1- percent of people has an IQ score between 74 and 126.

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Therefore 5% of people has an IQ score less than 74 or greater than 126.

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$\overline{x}+3\sigma=100+3(13)=139$

$[\overline{x}-3\sigma,\overline{x}+3\sigma]=[61,139]$

Using empirical rule we can say that 99.7% of people has an IQ score between 61 and 139.

The percentage of people has an IQ score less than 61 or greater than 139 is

P = 1- percent of people has an IQ score between 61 and 139.

P = 1- 99.7%

P = 0.3%

The percentage of people has an IQ score greater than 139 is

$P=\frac{1}{2}(0.3\%)=0.15\%$

Therefore 0.15% of people has an IQ score greater than 139.

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