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)=0.9707. 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)=0.9707. 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), (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 (P(-c\leq Z\leq c)=0.9707), so (2\Phi(c)-1 = 0.9707).

Step2: Solve for (\Phi(c))

First, solve the equation (2\Phi(c)-1 = 0.9707) for (\Phi(c)). Add 1 to both sides: (2\Phi(c)=0.9707 + 1=1.9707). Then divide both sides by 2: (\Phi(c)=\frac{1.9707}{2}=0.98535).

Step3: Find the value of (c)

Using a standard - normal table (or a calculator with a normal - distribution function), we find the (z) - value (c) such that (\Phi(c)=0.98535). Looking up in the standard - normal table, (c\approx2.17).

Answer:

(2.17)