Trading volume on the New York Stock Exchange is heaviest during the first half

Question

Trading volume on the New York Stock Exchange is heaviest during the first half hour (early morning) and last half hour (late afternoon) of the trading day. The early morning trading volumes (millions of shares) for 16 days in January and February are shown below. The probability distribution of trading volume is approximately normal. Label all answers appropriately. VOLUME:

a. Compute the mean and standard deviation to use as estimates of the population mean and standard deviation.

b. What is the probability that, on a randomly selected day, the early morning trading volume will be less than 180 million shares?

c. What is the probability that, on a randomly selected day, the early morning trading volume will exceed 200 million shares?

d. What is the probability that, on a randomly selected day, the early morning trading volume will be between 180 and 200 million shares?

d. How many shares would have to be traded for the early morning trading volume on a particular day to be among the busiest 5% of days?

179 208 217 200 184 160 245 201 209 210 177 212 210 194 180 165

Explanation / Answer

a) Data:

n= 15; sample mean = 196.975
Variance=²= 476.0625

b) z = ( x - ) / = -0.77628
P (x < 180.0000) = P (z < -0.77628)

c) P (200.0000 < x) = P (.14306< z) = 0.218792

d) P (180< x < 200 ) = P (-.77628 < z < .14306 ) =

179 208 217 200 184 160 245 201 209 210 177 212 210 194 180 165

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