# Probability Distribution

See the attached file.

1)

The time it takes for a light bulb to burn out.

Continuous

The weight of a t-bone steak

Continuous

The number of people in class who have type B blood.

Discrete

2) The mean (expected value) of the random variable is

3) The variance of the random variable is

4) The standard deviation of the random variable is

5) The probability that Apu sells exactly 8 tofu dogs in a day is

6) The probability that Apu sells 7 or more tofu dogs in a day is

7) Let X denote the payoff. Then X can take the following values

8) A simple random sample of 40 students are asked whether they have internet access at home. The number of students who do have home access is recorded

9) If X follows a binomial distribution with parameters n and p, the probability distribution of X is given by,

10) ) If X follows a binomial distribution with parameters n and p, the probability distribution of X is given by,

11) The mean of the random variable is

12) The standard deviation of the random variable is

13) The probability that x<4 is given by,

14) Let X denote the number of patients who experienced weight gain as a side effect in a random sample of 50.

15) The probability that 8 or fewer experienced weight gain as a side effect is given

16) The probability that 6 or more patients experienced weight gain as a side effect is

17) According to the range rule of thumb, most values should lie within 2 standard deviations from the mean. We can therefore identify "unusual" values by determining if they lie outside these limits:

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#### Solution Preview

Please see the attachment for solution.

Please see the Excel file for computation.

1)

The time it takes for a light bulb to burn out.

Continuous

The weight of a t-bone steak

Continuous

The number of people in class who have type B blood.

Discrete

2) The mean (expected value) of the random variable is

= 5.741

3) The variance of the random variable is

= 39.073 - (5.741)2

= 6.1139

= 6.114

4) The standard deviation of the random variable is

= 2.4726

= 2.473

5) The probability that Apu sells exactly 8 tofu dogs in a day is

P(x = 8) = P(8) = 0.076

6) The probability that Apu sells 7 or more tofu dogs in a day is

= P(7) + P(8) + P(9) + P(10) + P(11)

= 0.094 + 0.076 + 0.058 + 0.054 + 0.055

= 0.337

7) Let X denote the payoff. Then X can take the following values

X = $680 if the property in question will not be destroyed by a flood

= $680 - $800,000 = -$799,320, if the property will be destroyed by a flood

Here it is given that the probability that the property in question will be destroyed by a flood in the coming year is 0.0003265.

Thus the ...

#### Solution Summary

The solution discusses the application of various tools in statistics using probability theory.