Q1) Determine the following probabilities:

(a) Events A and B are mutually exclusive events defined on common sample space. If P (A) 0.5 and P(A or B) = 0.70, determine P(B).

(b) Events A and B are defined on the common sample space. If P(A) = 0.30, P(B) = 0.50, and P(A or B) = 0.72, determine P(A and B) 

Q2) According to new survey, Americans get the mean of 7 hours of sleep per night. Arbitrary sample of 50 students at West Virginia University disclosed mean number of hours slept last night was six hours and 48 minutes (6.8 hours). Standard deviation of sample was 0.9 hours. Is it sensible to conclude that students at West Virginia sleep less than typical American? Calculate the p-value.