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Chapter 5: Q9 (page 195)

In Exercises 7鈥�14, determine whether a probability

distribution is given. If a probability distribution is given, find its mean and standarddeviation. If a probability distribution is not given, identify the requirements that are notsatisfied.

Ted is not particularly creative. He uses the pickupline 鈥淚f I could rearrange the alphabet, I鈥檇 put U and I together.鈥漈he random variable xis the number of women Ted approachesbefore encountering one who reacts positively.

x

P(x)

1

0.001

2

0.009

3

0.030

4

0.060

Short Answer

Expert verified

The requirement that the sum of probabilities is equal to 1 is not satisfied.

Step by step solution

01

Given information

The probability distribution for the number of women Ted approaches before encountering one who reacts positively is given.

The variable x is the number of women Ted approaches before encountering one who reacts positively.

02

Identify the requirements for a probability distribution

The requirements are as follows.

1)The variable x is anumerical random variable.

2)The sum of the probabilities is computed as

鈭�Px=0.001+0.009+0.03+0.06=0.100

Therefore,the sum of the probabilities is not equal to 1 and the difference cannot be explained as roundoff error in the values

3) Each value of P(x) is between 0 and 1.

Thus, the requirement that the sum of probabilities is equal to 1 is not satisfied.

Therefore, the mean and standard deviation for the provided set cannot be computed.

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