Question

Determine the area under the standard normal curve that lies to the left of ​(a) Upper Z equals 0.23 comma ​(b) Upper Z equals 1.33​, ​(c) Upper Z equals negative 0.95​, and​ (d) Upper Z equals negative 1.14.

Answer 1

Answer:

a) $P(Z<0.23) = 0.591$

"=NORM.DIST(0.23,0,1,TRUE)"

b) $P(Z<1.33) = 0.908$

"=NORM.DIST(1.33,0,1,TRUE)"

c) $P(Z<-0.95) = 0.171$

"=NORM.DIST(-0.95,0,1,TRUE)"

d) $P(Z<-1.14) = 0.127$

"=NORM.DIST(-1.14,0,1,TRUE)"

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

For this case we can find the areas using the standard normal table or Excel, for this case we will use excel command NORM.DIST who gives the area on the left area of a given value, and we provide the code for each case:

a) $P(Z<0.23) = 0.591$

"=NORM.DIST(0.23,0,1,TRUE)"

b) $P(Z<1.33) = 0.908$

"=NORM.DIST(1.33,0,1,TRUE)"

c) $P(Z<-0.95) = 0.171$

"=NORM.DIST(-0.95,0,1,TRUE)"

d) $P(Z<-1.14) = 0.127$

"=NORM.DIST(-1.14,0,1,TRUE)"