Given a standard normal distribution, what is the area to the left of $1.25$? (Round your answer to 4 decimal places.)

• A. $0.8944$
• B. $0.6915$
• C. $0.7734$
• D. $0.1056$

Answer: (A)

Verified step by step guidance

1. Recognize that the problem asks for the cumulative probability to the left of a z-score in a standard normal distribution. This means we want to find \(P(Z < 1.25)\) where \(Z\) follows a standard normal distribution with mean 0 and standard deviation 1.
2. Understand that the area to the left of a z-score corresponds to the cumulative distribution function (CDF) value at that z-score. Mathematically, this is \(\Phi(1.25)\), where \(\Phi\) is the CDF of the standard normal distribution.
3. Use a standard normal distribution table, a calculator with statistical functions, or software to find the value of \(\Phi(1.25)\). This value represents the probability that a standard normal random variable is less than 1.25.
4. Locate the row for 1.2 and the column for 0.05 in the z-table (since 1.25 = 1.2 + 0.05) to find the cumulative probability corresponding to 1.25.
5. Round the obtained cumulative probability to 4 decimal places as requested to get the final answer.