Find the following probability for the standard normal random variable z. a. P(z = 3) b. P(zs3) e. P(-3szs3) c. P(z<3) d. P(z>3) f. P(-2szs2) g. P(- 2.91 szs0.98) h. P(-0.57 3) = 0.001 (Round to three decimal places as needed.) e. P(-3szs3) = 0.997 (Round to three decimal places as needed.) f. P(-2szs2) = (Round to three decimal places as needed.)

Tutorial Exercise Given that z is a standard normal random variable, compute the following probabilities. (a) P(-1.95 sz s 0.46) (b) P(0.55 sz s 1.23) (c) P(-1.85 ≤zs -1.05) Step 1 (a) P(-1.95 sz≤ 0.46) For z to be a standard normal variable means that the random variable z follows a normal distribution with mean 0 and standard deviation 1. The normal distribution is a bell-shaped curve that is symmetric about the mean. The graph of a standard normal curve is below. -3 -2 -1 0 mean, " z -2.0 -1.9 1 This distribution is continuous, so probabilities will be for a range of values and represented by the area under the graph between the values. The desired probability is for the region between z = -1.95 and z = 0.46. Since z = -1.95 is to the left of z = 0.46, we can find this probability by subtracting the area under the curve to the left of z = -1.95 2 3 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192 0.0188 0.0183 0.0287 0.0281…

Let Z be a standard normal random variable. Calculate the following probabilities and round your response to at least 3 decimal places. P(Z is less than or equal to -2.12)=        P(Z>-0.71)=         P(0.92<Z<2.09)=