Final answer:
To find the percentage of preterm infants with specific arterial cord pH levels, calculate the z-scores for given pH values and use these to determine the percentages from the standard normal distribution table. For pH levels between 7.00 and 7.50, find the difference in percentages for these levels. For pH levels over 7.37, subtract the percentage corresponding to this level from 100%.
Step-by-step explanation:
The question asks for the percentage of preterm infants with certain arterial cord pH levels, assuming that these levels are normally distributed with a mean of 7.29 and a standard deviation of 0.16. To find these percentages, the z-score formula (z = (X - μ) / σ, where X is the pH level, μ is the mean, and σ is the standard deviation) can be used, followed by consulting a standard normal distribution table or using calculator functions.
a. To calculate the percentage of preterm infants with arterial cord pH levels between 7.00 and 7.50
- First, calculate the z-scores for pH 7.00 and pH 7.50.
- Then, find the corresponding percentages for these z-scores in the standard normal distribution table.
- Finally, subtract the percentage corresponding to pH 7.00 from that of pH 7.50 to find the percentage between these two levels.
b. To calculate the percentage of preterm infants with arterial cord pH levels over 7.37:
- Calculate the z-score for pH 7.37.
- Find the percentage that corresponds to this z-score.
- Subtract this percentage from 100% to find the percentage of infants with a pH level over 7.37.