if Z is a standard normal variable, find the probability.

the probability that z lies between -2.41 and 0

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion between those two Z scores. I got .492.

Remember that Z = 0 is the mean.

Find the indicated area under the standard normal curve to the right of Z= -2.55 curve is what

To find the probability that a standard normal variable Z lies between -2.41 and 0, we need to calculate the area under the standard normal curve between these two values.

Step 1: Look up the respective Z-scores for -2.41 and 0.

The Z-score for -2.41 can be found using a Z-table or a statistical calculator. From the table, we find that the Z-score for -2.41 is approximately 0.0082.

The Z-score for 0 is 0 since it represents the mean of the standard normal distribution.

Step 2: Calculate the probability.

To find the probability between -2.41 and 0, subtract the Z-score for -2.41 from the Z-score for 0.

P(-2.41 < Z < 0) = P(Z < 0) - P(Z < -2.41)
= 0 - 0.0082
≈ 0.0082

Therefore, the probability that Z lies between -2.41 and 0 is approximately 0.0082.

To find the probability that a standard normal variable, denoted as Z, lies between -2.41 and 0, we need to calculate the area under the standard normal curve corresponding to this interval.

1. Convert the values -2.41 and 0 to Z-scores:
- The Z-score formula is Z = (X - μ) / σ, where X is the given value, μ is the mean, and σ is the standard deviation.
- Since Z is a standard normal variable, its mean is 0 and the standard deviation is 1. Therefore, the Z-scores are -2.41/1 = -2.41 and 0/1 = 0.

2. Look up the corresponding area under the standard normal curve for each Z-score:
- The area under the standard normal curve can be obtained using statistical tables or with the help of statistical software.
- For -2.41, the area to the left of it is given by the standard normal table or software (e.g., 0.0073).
- For 0, the area to the left of it is 0.5000 (which can be obtained from the standard normal table).

3. Calculate the probability between the two Z-scores:
- Subtract the smaller area from the larger area:
Probability = Area(Z ≤ 0) - Area(Z ≤ -2.41)

- Probability = 0.5000 - 0.0073 = 0.4927 (rounded to four decimal places).

Therefore, the probability that Z lies between -2.41 and 0 is approximately 0.4927.