Question

Suppose Z follows the standard normal distribution. Use the calculator provided, to determine the value of c so that the following is trae. P(1.11≤Z≤c)=0.0917 Carry your intermediate computations to at Ieast four decimal places. Round your answer to two decimal places.

Answer 1

To find the value of c for P(1.11≤Z≤c)=0.0917, use the cumulative area for Z=1.11 and add 0.0917, then use invNorm to get the corresponding Z-score which is c.

Step-by-step explanation:

To determine the value of c where P(1.11≤Z≤c)=0.0917, we first find the cumulative probability for Z=1.11 using a standard normal distribution table or calculator. This is the area under the curve to the left of Z=1.11. Then we add 0.0917 to this cumulative probability to get the total area to the left of Z=c. We use the invNorm function on a calculator, such as invNorm(area,0,1), to find the corresponding Z-score for this cumulative area, which gives us our value for c. For example, if the area to the left of Z=1.11 is 0.8665, we calculate invNorm(0.8665 + 0.0917,0,1) to find the value of c with at least four decimal precision and then round it to two decimal places.