A baseball player is asked to swing at pitches in sets of four. The player swings at 100 sets of 4 pitches. Theprobability distribution for hitting a particular number of pitches is given below. Determine the standarddeviation for this discrete probability distribution. $$\begin{array} { | c | c | c | c | c | c | }
\hline x & 0 & 1 & 2 & 3 & 4 \
\hline P ( x ) & 0.02 & 0.07 & 0.22 & 0.27 & 0.42 \
\hline
\end{array}$$
A) 1.05
B) 1.10
C) 1.21
D) 0.28

Question

A baseball player is asked to swing at pitches in sets of four. The player swings at 100 sets of 4 pitches. Theprobability distribution for hitting a particular number of pitches is given below. Determine the standarddeviation for this discrete probability distribution. $$\begin{array} { | c | c | c | c | c | c | } 
\hline x & 0 & 1 & 2 & 3 & 4 \
\hline P ( x ) & 0.02 & 0.07 & 0.22 & 0.27 & 0.42 \
\hline
\end{array}$$
A) 1.05
B) 1.10
C) 1.21
D) 0.28

Quizplus · Accepted Answer

The standard deviation for this discrete probability distribution is 1.05. This can be calculated using the formula:σ = √(Σ(x - μ)²P(x))where x is the number of pitches hit, μ is the mean, and P(x) is the probability of hitting x pitches.The mean can be calculated as:μ = Σ(xP(x)) = (0 * 0.02) + (1 * 0.07) + (2 * 0.22) + (3 * 0.27) + (4 * 0.42) = 2.68The variance can then be calculated as:σ² = Σ((x - μ)²P(x)) = ((0 - 2.68)² * 0.02) + ((1 - 2.68)² * 0.07) + ((2 - 2.68)² * 0.22) + ((3 - 2.68)² * 0.27) + ((4 - 2.68)² * 0.42) = 1.1088And the standard deviation is:σ = √(1.1088) = 1.05

A Baseball Player Is Asked to Swing at Pitches in Sets