A census was conducted at a university. All students were asked how many tattoos

Question

A census was conducted at a university. All students were asked how many tattoos they had.

The table below presents a probability distribution for the discrete variable of number of tattoos for each student. From this table we can find that 85% of students in the population do not have a tattoo, 12% of students in the population have one tattoo, 1.5% of students in the population have two tattoos, and so on.

0

1

2

3

4

.850

.120

.015

.010

.005

Figure 2. Probability Distribution for Number of Tattoos Each Student Has in a Population of Students Tattoos

0

1

2

3

4

Probability

.850

.120

.015

.010

.005

c. Compute the mean, variance, and the standard deviation of the distribution. d. What is the probability that Xis within one standard deviation of the mean? xis within two standard deviations of the mean? (ii) Xis within three standard deviations of the mean?

Explanation / Answer

iv. P(atmost 2) = 0.850 + 0.12 + 0.015 = 0.985

c.

f=   1  
fx =   0.2  
      
Mean = fx / f =   0.2  
Mean square = f x^2 / f =   0.35  
      
Varriance = (Mean square) - (Mean)^2      
      
Varriance = f x^2 - Mean^2 =   0.31  
Stadard Dev= Var =   0.557  

Values ( X ) Frequency(f) fx ( X^2) f x^2 0 0.85 0 0 0 1 0.12 0.12 1 0.12 2 0.015 0.03 4 0.06 3 0.01 0.03 9 0.09 4 0.005 0.02 16 0.08

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