Question

Let X be a standard normal random variable. Find P(-1.20 < X < 1.74). Express your answer as a decimal.

Answer 1

To find \( P(-1.20 < X < 1.74) \) for a standard normal random variable \( X \), we can use the cumulative distribution function (CDF) of the standard normal distribution.

1. First, find the cumulative probabilities for \( X = -1.20 \) and \( X = 1.74 \).

Using a standard normal distribution table or a calculator:

- The value of \( P(X < -1.20) \) is approximately \( 0.1151 \).
- The value of \( P(X < 1.74) \) is approximately \( 0.9591 \).

2. Now, we can find the probability \( P(-1.20 < X < 1.74) \) using the formula:

\[
P(-1.20 < X < 1.74) = P(X < 1.74) - P(X < -1.20)
\]

Substituting the values:

\[
P(-1.20 < X < 1.74) = 0.9591 - 0.1151
\]

Calculating this gives:

\[
P(-1.20 < X < 1.74) = 0.8440
\]

Therefore, the final answer is:

\[
\boxed{0.8440}
\]