Answer :
To find the area of the standard normal distribution between two z-scores, we perform the following steps:
1. **Find the cumulative distribution function (CDF) value for both z-scores**: The standard normal distribution is a special case of the normal distribution where the mean is 0 and the standard deviation is 1. The CDF gives us the area under the curve to the left of a given z-score.
2. **Subtract the CDF of the smaller z-score from the CDF of the larger z-score**: The area between two z-scores in a normal distribution is found by subtracting the CDF value of the lower z-score from the CDF value of the higher z-score.
So, let's perform these steps using standard normal distribution tables, which provide the cumulative probability associated with a given z-score.
For z = 1.24:
- Look up the CDF value for z = 1.24 in the standard normal distribution table. If you do not have a table handy, you could use a calculator or software that provides the CDF. The value for z = 1.24 is approximately 0.8925.
For z = 1.73:
- Look up the CDF value for z = 1.73 in the standard normal distribution table. If you do not have a table handy, you could use a calculator or software that provides the CDF. The value for z = 1.73 is approximately 0.9582.
Now, subtract the CDF value of z = 1.24 from the CDF value of z = 1.73:
Area = CDF(z = 1.73) - CDF(z = 1.24)
Area = 0.9582 - 0.8925
Area = 0.0657
The area between the z-scores 1.24 and 1.73 in the standard normal distribution, rounded to the nearest thousandth, is 0.066.
Remember that this calculation assumes that you have accurate CDF values from a standard normal distribution table or from a computational tool that provides these values. If you're using a different source, your values might vary slightly.
