Which of the following percentages accurately estimates the area under a normal curve between a z-score of −0.11

and 2.43?(1 point)
Responses

99.25 percent
99.25 percent

53.63 percent
53.63 percent

45.62 percent
45.62 percent

54.38 percent

1 answer

To find the area under a normal curve between a z-score of -0.11 and 2.43, we can look up the cumulative probabilities for these two z-scores using a standard normal distribution table or a calculator.

  1. For \( z = -0.11 \): the cumulative probability (area to the left) is approximately \( 0.4562 \) or \( 45.62% \).
  2. For \( z = 2.43 \): the cumulative probability (area to the left) is approximately \( 0.9925 \) or \( 99.25% \).

To find the area between these two z-scores, we subtract the cumulative probability at -0.11 from the cumulative probability at 2.43:

\[ \text{Area between } z = -0.11 \text{ and } z = 2.43 = P(Z < 2.43) - P(Z < -0.11) \]

\[ = 0.9925 - 0.4562 = 0.5363 \]

Converting this to a percentage gives:

\[ 0.5363 \times 100 = 53.63% \]

Thus, the area under the normal curve between a z-score of -0.11 and 2.43 is approximately 53.63 percent.

So the correct response is:

53.63 percent