finding the cumulative probability using the z-scores.
Using a calculator or a standard normal distribution table, we can find the z-scores corresponding to each value:
z₁ = (5 - 5.5) / 1.2
z₂ = (8 - 5.5) / 1.2
Then, we find the cumulative probability for each z-score:
P₁ = P(Z < z₁)
P₂ = P(Z < z₂)
Finally, we subtract P₁ from P₂ to find the desired probability, and then multiply it by the total number of babies (1100) to get the expected count.
Expected count = (P₂ - P₁) * 1100
2. To calculate the number of newborn babies expected to weigh less than 7 pounds, we need to find the cumulative probability up to 7 pounds. We can find the z-score for 7 pounds and calculate the cumulative probability:
z = (7 - 5.5) / 1.2
P = P(Z < z)
Then, we multiply this probability by the total number of babies (1100) to get the expected count.
Expected count = P * 1100
3. To calculate the number of newborn babies expected to weigh more than 6 pounds, we need to find the cumulative probability beyond 6 pounds. We can find the z-score for 6 pounds and calculate the cumulative probability:
z = (6 - 5.5) / 1.2
P = P(Z > z)
Then, we multiply this probability by the total number of babies (1100) to get the expected count.
Expected count = P * 1100
4. To calculate the number of newborn babies expected to weigh between 5.5 and 9 pounds, we can follow the same process as in question 1, using the z-scores for each boundary and calculating the difference in cumulative probabilities:
z₁ = (5.5 - 5.5) / 1.2
z₂ = (9 - 5.5) / 1.2
P₁ = P(Z < z₁)
P₂ = P(Z < z₂)
Expected count = (P₂ - P₁) * 1100