Let ? ?be a standard normal random variable and calculate the following probabilities, drawing pictures wherever appropriate.

Answer : Step 1 of 10 : Let Z be a standard normal random variable The claim is to calculate the probabilities a) We have to find the probability values for P(0 Z 2.17) Let, P(0 Z 2.17) = (2.17) - (0) We have to check standard normal table for the values 2.17 and 0 Therefore, P(0 Z 2.17) = 0.9850 - 0.5000 = 0.4850 Hence, P(0 Z 2.17) = 0.4850. Step 2 of 10 : b) We have to find the probability values for P(0 Z 1) Let, P(0 Z 1) = (1) - (0) We have to check standard normal table for the values 1 and 0 Therefore, P(0 Z 1) = 0.8413 - 0.5000 = 0.3413 Hence, P(0 Z 1) = 0.3413 Step 3 of 10 : c) We have to find the probability values for P(-2.50 Z 0) Let, P(-2.50 Z 0) = (0) - (-2.50) We have to check standard normal table for the values -2.50 and 0 Therefore, P(-2.50 Z 0) = 0.5000 - 0.0062 = 0.4938 Hence, P(-2.50 Z 0) = 0.4938 Step 4 of 10 : d) We have to find the probability values for P(-2.50 Z 2.50) Let, P(-2.50 Z 2.50) = (2.50) - (-2.50) We have to check standard normal table for the values 2.50 and -2.50 Therefore, P(-2.50 Z 2.50) = 0.9938 - 0.0062 = 0.9876 Hence, P(-2.50 Z 2.50) = 0.9876 Step 5 of 10 : e) We have to find the probability values for P( Z 1.37) Let, P( Z 1.37) = (1.37) We have to check standard normal table for the values 1.37 Therefore, P( Z 1.37) = (1.37) = 0.9147 Hence, P( Z 1.37) = 0.9147