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A child psychologist is interested in the number of times a newborn baby's crying wakes its...

A child psychologist is interested in the number of times a newborn baby's crying wakes its mother after midnight and so a random sample is conducted of 50 mothers. Two said 0 times, eleven said 1 time, twenty three said 2 times, nine said 3 times, four said 4 times, and one said 5 times. Let X = the number of times a newborn wakes its mother after midnight. Then for this sample, x = 0, 1, 2, 3, 4, 5.

a) Construct a table showing the frequency and the probability for each value of X.
b) Construct a histogram of the probability distribution.
c) Find the expected value μ for the number of times a newborn baby's crying wakes its mother after midnight.
d) Calculate the standard deviation σ for this probability distribution.


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