Suppose Z follows the standard normal distribution. Use your z table, to determine the value of c so that the following is true.2 points0.10.30.50.7

1. Break Down the Problem

We need to find the value of $c$ such that $P(Z < c) = p$ for given probabilities $p$ of 0.10, 0.30, 0.50, and 0.70.

2. Relevant Concepts

For a standard normal distribution:

• The Z-table, also known as the standard normal table, provides the cumulative probabilities $P(Z < c)$ for various values of $c$.

3. Analysis and Detail

Using the Z-table, we will look up the values corresponding to the given probabilities:

1. For $P(Z < c) = 0.10$:

   • From the Z-table, find the value of $c$ that corresponds to a cumulative probability of 0.10.
   • The value is approximately $c \approx -1.28$.

2. For $P(Z < c) = 0.30$:

   • Similarly, find the value of $c$ that corresponds to a cumulative probability of 0.30.
   • The value is approximately $c \approx -0.52$.

3. For $P(Z < c) = 0.50$:

   • For the median of the standard normal distribution, since $P(Z < 0) = 0.50$, we find:
   • The value is $c = 0.00$.

4. For $P(Z < c) = 0.70$:

   • Find the value of $c$ that corresponds to a cumulative probability of 0.70.
   • The value is approximately $c \approx 0.52$.

4. Verify and Summarize

The values we found correspond to the specified probabilities in the Z-table. Each value satisfies the condition $P(Z < c) = p$.

Final Answer

The values of $c$ for the given probabilities are:

• For $0.10$: $c \approx -1.28$
• For $0.30$: $c \approx -0.52$
• For $0.50$: $c = 0.00$
• For $0.70$: $c \approx 0.52$