Question

Suppose Z follows the standard normal distribution. Use the calculator provided, or this table, to determine the value of c so that the following is true. P(c≤Z≤-0.87)=0.1786. Carry your intermediate computations to at least four decimal places. Round your answer to two decimal places.

Answer 1

To find the value of c, use the standard normal distribution table or calculator. P(c≤Z≤-0.87) = 0.1786. The value of c is approximately -0.53.

Step-by-step explanation:

To find the value of c, we need to use the standard normal distribution table or a calculator. We know that P(c≤Z≤-0.87) = 0.1786. From the table or calculator, we find that the area to the left of -0.87 is 0.1949. Subtracting this from 0.5 (the area to the left of 0 in the standard normal distribution) gives us 0.3051.

Since the left tail area is 0.3051, we need to find the z-value that has a left tail area of 0.3051. By looking up the z-value corresponding to this area, we can find the value of c. From the table or calculator, we find that the z-value for a left tail area of 0.3051 is approximately -0.53.

Therefore, the value of c is -0.53.