In 2014, the New York Yankees had a team batting average of -245 (actually 0.245

Question

In 2014, the New York Yankees had a team batting average of -245 (actually 0.245, but for simplicity, the decimal point is omitted here). Of course, the batting average varies from game to game, but assuming that the distribution of batting averages for 162 games is normal with a standard deviation of = 40 points, answer each of the following. Standard Normal Distribution Mean = 0.0 Standard Deviation 1.0 1303 8697 3.0 2.0 0.0 1.0 2.0 3.0 1.125 If you randomly select one game from 2014, what is the probability that the team batting average was over 300? p= 0.8460 If you randomly select one game from 2014, what is the probability that the team batting average was under 200? p0.1303

Explanation / Answer

a)

(i)probabilityof average over 300

(ii) probabilityof average below 200

2)

(i) score less than 400

(ii)

(iii) for highest 20% ; at 80th percentile z score =0.8416

hence corresponding value =mean +z*std deviation =500+0.8416*100 =584

(iv)

for 60th percentile ; zscore =0.2533

hence corresponding value =mean +z*std deviation =500+0.2533*100 =525

for normal distribution z score =(X-)/ here mean=       = 245.000 std deviation   == 40.00

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