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1. The average number of late students in a day is calculated by multiplying each number of late students by its probability, then summing up these products. Therefore, the calculation is as follows:
Average = (1*0.1) + (2*0.26) + (3*0.3) + (4*0.04) + (5*0.3)
Average = 0.1 + 0.52 + 0.9 + 0.16 + 1.5
Average = 3.18
Therefore, the average number of late students in a day is 3.18.
2. The probability distribution of the number of credit cards people own does not have a mean of 2. To find the mean, we multiply each number of credit cards by its probability and sum these products. The calculation is as follows:
Mean = (0*0.17) + (1*0.32) + (2*0.38) + (3*0.08) + (4*0.05)
Mean = 0 + 0.32 + 0.76 + 0.24 + 0.2
Mean = 1.52
Thus, the mean number of credit cards people own based on the given distribution is 1.52, not 2 as assumed by the bank president.