Use a table of cumulative areas under the normal curve to fi

Use a table of cumulative areas under the normal curve to find the z-score that corresponds to the given cumulative area. If the area is not in the table, use the entry closest to the area. If the area is halfway between two entries. use the z-score halfway between the corresponding z-scores. If convenient, use technology to find the z-score. 0.054 The cumulative area corresponds to the z-score of . (Round to three decimal places as needed.)

Solution

let Z~N(0,1)

the cummulative area=F(z)=P[Z<z]

we have to find z for which F(z)=0.047

now F(z)=0.047 so F(-z)=1-F(z)=1-0.047=0.953

so P[Z<-z]=0.953

from the table we get P[Z<1.674]=0.9525403 and P[Z<1.68]=0.9535213

now |0.9525403-0.953|<|0.9535213-0.953|

so 0.9525403 is closest to 0.953

so we take P[Z<1.674]=0.953 but we have taken P[Z<-z]=0.953

so -z=1.674 or, z=-1.674

hence P[Z<-1.674]=1-0.953=0.047

hence the z score is -1.674 [answer]

hence