Given that z has a standard normal distribution calculate th

Given that z has a standard normal distribution calculate the probability that z lies within 2.25 standard deviations of the mean z lies more than 1.5 standard deviation from the mean. Use Cumulative probability table. P(z lies within 2.25 standard deviations of the mean) = Q (Round to four decimal places as needed.) P(z lies more than 1.5 standard deviations from the mean) = (Round to four decimal places as needed.)

Solution

z has a standard normal distribution. so mean of z is 0 and standard deviation of z is 1.

a) P[0-2.25*1<z<0+2.25*1]=P[-2.25<z<2.25]=P[z<2.25]-P[z<-2.25]=0.987776-0.012224=0.975552 [answer]

[using cummulative probability table]

b) P[z>0+1.5*1]=P[z>1.5]=1-P[z<1.5]=1-0.933193=0.066807 [answer]

[from the language of part b it is confusing whether we need to calculate P[Z>1.5] or p[Z>0-1.5*1]=P[z>-1.5]

so i am providing ths answer also. p[z>-1.5]=0.933193 ]