The data in the table below are 60 smiling times, in seconds, of a four-week-old baby.

0.92 12.77 18.25 8.47 6.75 0.40 11.01 5.57 14.98 2.85

4.58 1.48 13.52 11.55 5.17 16.12 2.34 10.05 13.75 16.12

7.32 8.50 7.79 4.23 2.60 15.77 6.45 18.92 5.32 2.36

5.45 17.19 1.31 14.90 14.66 6.04 12.97 6.83 3.09 18.02

10.14 13.51 0.51 17.36 2.44 7.89 14.30 3.23 10.61 9.82

7.79 18.86 9.73 7.42 14.56 0.63 4.05 13.62 16.10 11.26

(a) We will assume that the smiling times, in seconds, follow a uniform distribution between zero and 20 seconds, inclusive. This means that any smiling time from zero to and including 20 seconds is equally likely. State the values of b and c. Write the distribution in proper notation, and calculate the theoretical mean and standard deviation.

(b) What is the probability that a randomly chosen four-week-old baby smiles between five and ten seconds?

(c) 80% of the time, a randomly selected baby would smile below what value?