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)=0.9371. 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)=0.9371. 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 distribution

Since the standard - normal distribution is symmetric about (z = 0), we know that (P(-c\leq Z\leq c)=2P(0\leq Z\leq c)). So, (2P(0\leq Z\leq c)=0.9371), then (P(0\leq Z\leq c)=\frac{0.9371}{2}=0.46855).

Step2: Find the (z) - value in the standard - normal table

We know that (P(Z\leq c)=P(Z\leq0)+P(0\leq Z\leq c)). Since (P(Z\leq0) = 0.5), then (P(Z\leq c)=0.5 + 0.46855=0.96855). Looking up this value in the standard - normal table (the (z) - table), we find the (z) - value corresponding to a cumulative probability of (0.96855).

Answer:

(c\approx1.86)