suppose z follows the standard normal distribution. use the calculator provided, or this table, to determine…

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 ≤ c)=0.9164. carry your intermediate computations to at least four decimal places. round your answer to two decimal places.

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 ≤ c)=0.9164. carry your intermediate computations to at least four decimal places. round your answer to two decimal places.

Answer

Explanation:

Step1: Use symmetry of standard - normal

Since the standard - normal distribution is symmetric about (z = 0), we know that (P(-c\leq Z\leq c)=2\Phi(c)- 1), where (\Phi(c)) is the cumulative distribution function of the standard - normal distribution. We are given that (2\Phi(c)-1 = 0.9164).

Step2: Solve for (\Phi(c))

First, solve the equation (2\Phi(c)-1 = 0.9164) for (\Phi(c)). Add 1 to both sides: (2\Phi(c)=0.9164 + 1=1.9164). Then divide both sides by 2: (\Phi(c)=\frac{1.9164}{2}=0.9582).

Step3: Find (c) using the standard - normal table

Looking up the value (0.9582) in the standard - normal table (or using a calculator with a normal - distribution function), we find the (z) - value corresponding to this cumulative probability. The (z) - value (i.e., (c)) such that (\Phi(c)=0.9582) is approximately (1.73).

Answer:

(1.73)