Given that z has a standard normal distribution calculate th

Given that z has a standard normal distribution calculate the probability that (a) z lies within 1-5 standard deviations of the mean (b) z lies more than 2.5 standard deviation from the mean. Use Cumulative probability table. (a) P(z lies within 1.5 standard deviations of the mean) (Round to four decimal places as needed.) (b) P (z lies more than 2.5 standard deviations from the mean) = (Round to four decimal places as needed.)

Solution

(a)now, z=1.5, find 1.5 in th z column, the table entry is 0.4332.

Thus, P(z lies 1.5 standard deviations of the mean)=0.4332.

(b)Z=2.5, the table entry is 0.9798.

Thus, P(z lies 2.5 standard deviations of the mean)=0.9798.