The frequency of color blindness (dyschromatopsia) in the Caucasian American male population is estimated to be about 8%. Let's call X the number of color-blind individuals in a random sample of 8 Caucasian American males. The table gives the probability distribution for X.
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$$\begin{array} { | l | l | l | l | l | l | l | l | l | l | }
\hline X & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \
\hline P ( X ) & 0.513 & 0.357 & 0.109 & 0.019 & 0.002 & 0.000 & 0.000 & 0.000 & 0.000 \
\hline
\end{array}$$ What is the mean of this distribution?

Question

The frequency of color blindness (dyschromatopsia) in the Caucasian American male population is estimated to be about 8%. Let's call X the number of color-blind individuals in a random sample of 8 Caucasian American males. The table gives the probability distribution for X.
?
?
$$\begin{array} { | l | l | l | l | l | l | l | l | l | l | } 
\hline X & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \
\hline P ( X ) & 0.513 & 0.357 & 0.109 & 0.019 & 0.002 & 0.000 & 0.000 & 0.000 & 0.000 \
\hline
\end{array}$$ What is the mean of this distribution?

Quizplus · Accepted Answer

The mean of a binomial distribution is calculated as $ n \times p $, where $ n $ is the number of trials (8 in this case) and $ p $ is the probability of success (0.08). Thus, the mean is $ 8 \times 0.08 = 0.64 $.

The Frequency of Color Blindness (Dyschromatopsia) in the Caucasian American