Question

Find the area under the standard normal curve to the left of

z=−1.52. Draw the standard normal curve.
A)
≈0.0643

B)
≈0.9357

C)
≈0.4364

D)
≈0.9357

Answer 1

The area under the standard normal curve to the left of

z=−1.52 is:

B) ≈0.0643

Step-by-step explanation:

The standard normal distribution, often represented by the z-score, has a mean (μ) of 0 and a standard deviation (σ) of 1. To find the area under the standard normal curve to the left of z=−1.52, we consult a standard normal distribution table or a calculator. The value corresponds to the cumulative probability of observing a z-score less than -1.52.

The negative z-score indicates a position to the left of the mean on the standard normal curve. From the standard normal distribution table, we find that the cumulative probability for z=−1.52 is approximately 0.0643. This means that approximately 6.43% of the data falls to the left of z=−1.52 in a standard normal distribution.

In summary, option B) ≈0.0643 is the correct answer, representing the area under the standard normal curve to the left of z=−1.52. This result indicates the probability of observing a standard normal random variable less than -1.52, providing valuable insights into the distribution of data in a standard normal distribution.