High School

The lengths of babies born at Tarth Hospital in the last year were normally distributed. The mean length was 50 cm and the standard deviation was 3.5 cm.

What proportion of babies are shorter than 46.5 cm?

Answer :

Final answer:

To find the proportion of babies shorter than 46.5 cm in a normally distributed population with a mean of 50 cm and a standard deviation of 3.5 cm, we can use the Z-score formula. The proportion is approximately 0.1587.

Explanation:

To solve this problem, we can use the Z-score formula: Z = (X - μ) / σ, where X is the value we want to find the proportion for, μ is the mean, and σ is the standard deviation.

Plugging in the values from the question, we get: Z = (46.5 - 50) / 3.5 = -1

To find the proportion of babies shorter than 46.5 cm, we need to find the area to the left of Z = -1 on a standard normal distribution table.

Based on the table, the proportion is approximately 0.1587.