Q3

3 . We would like to estimate the true mean size * ( in square feet ) of all two -bedroom apartments in Winnipeg . A random sample of 30 two -bedroom apartments in the city is selected , and the mean size of these apartments is calculated to be 1000 square feet . Suppose it is known that sizes of two -bedroom apartments in the city follow a normal distribution with standard deviation 200 square feet . ( 2 ) Calculate a 93% confidence interval for the true mean size of all two -bedroom apart- ments in Winnipeg . ( b ) Interpret the meaning of the interval you calculated in ( a ) .2. Consider the following information about three events A, B and C: la . P(A) = 0.43 REXPW : 0.31v0.28 - 0 . 10 34 P(C) = 0.28 P(AnB) - 0.19 PLATXP(B) - 6. 3790.43 = 0.16 P(BnC) - 0.12 PLAXICO = O .1804 P(AU B) = 0.61 . P(AUC) = 0.71 PCAUC) - PLA)+ PLC)-CANC 0. 71 = 0.43+0.28 (a) What is P(B)? AnC - O (b) Are any two of the three events mutually exclusive? A and C is mutuallyexclusive (c) Are any two of the three events independent? A and & , BandCAand & not 'ndepodat Ad) What is the probability that exactly one of the three events occurs