Answer:
We can use the normal distribution to estimate the number of babies that weighed less than 3.2 kg and between 2.8 kg and 3.4 kg. We will assume that the weights of the babies are normally distributed.
Explanation:
a) To estimate the number of babies that weighed less than 3.2 kg, we can use the z-score formula:
z = (x - μ) / σ
where x is the weight we want to estimate (3.2 kg), μ is the mean weight (3.0 kg), and σ is the standard deviation (0.2 kg).
z = (3.2 - 3.0) / 0.2 = 1
We can look up the probability corresponding to a z-score of 1 in a standard normal distribution table or use a calculator. The probability of a baby weighing less than 3.2 kg is approximately 0.8413.
So, the estimated number of babies that weighed less than 3.2 kg is:
0.8413 x 545 = 458.9
We can round this to the nearest whole number and estimate that about 459 babies weighed less than 3.2 kg.
b) To estimate the number of babies that weighed between 2.8 kg and 3.4 kg, we can use the same formula and find the probabilities corresponding to the z-scores for 2.8 kg and 3.4 kg.
z1 = (2.8 - 3.0) / 0.2 = -1
z2 = (3.4 - 3.0) / 0.2 = 2
The probability of a baby weighing less than 2.8 kg (corresponding to a z-score of -1) is approximately 0.1587. The probability of a baby weighing less than 3.4 kg (corresponding to a z-score of 2) is approximately 0.9772. So, the probability of a baby weighing between 2.8 kg and 3.4 kg is:
0.9772 - 0.1587 = 0.8185
The estimated number of babies that weighed between 2.8 kg and 3.4 kg is:
0.8185 x 545 = 446.2
We can round this to the nearest whole number and estimate that about 446 babies weighed between 2.8 kg and 3.4 kg.