The value of the normal distribution at Z is 0.8770. The value of Z is _______.Question 10Select one:a.1.16b.0.18c.0.81d.1.47

Break Down the Problem

1. We need to find the value of $Z$ such that the cumulative probability $P(Z \leq z) = 0.8770$.
2. The options provided are:
   • a. $1.16$
   • b. $0.18$
   • c. $0.81$
   • d. $1.47$

Relevant Concepts

1. The cumulative distribution function (CDF) of a standard normal distribution can be used to find the $Z$ value corresponding to a given probability.
2. We can refer to a Z-table or use statistical software to find which $Z$ corresponds to the cumulative probability of $0.8770$.

Analysis and Detail

1. Looking at a Z-table or using a calculator that provides normal distribution probabilities, we need to find the value $z$ for which $P(Z \leq z) = 0.8770$.
2. Checking the Z-table:
   • $Z = 1.16$ corresponds to $P(Z \leq 1.16) \approx 0.8770$
   • Other options will yield either a lower or higher probability.

Verify and Summarize

1. Comparing the found probabilities,
   • $P(Z \leq 1.16) = 0.8770$
   • The values $0.18$, $0.81$, and $1.47$ do not correspond to $0.8770$ in standard Z-tables.
2. Thus, the only match for $0.8770$ is $Z = 1.16$.

Final Answer

The value of $Z$ is 1.16.