Question

9. The lengths of pregnancies are normally distributed with a mean of 268 days and a standarddeviation of 15 days. A baby is premature if the length of pregnancy is in the lowest 7%. Findthe length of pregnancy (number of days) that separates premature babies from those who are notpremature.

Answer 1

Answer:

The length of pregnancy that separates premature babies from those who are not premature is approximately 269

Step-by-step explanation:

The length of pregnancies is given as 268 days, and the standard deviation is 15 days.

We want to find the length that separates premature babies from those who are not premature, we use the Z transform

`\begin{gathered} Z=(x-\mu)/(\sigma) \\ \\ \mu=268 \\ \sigma=15 \\ \\ 0.07=(x-268)/(15) \\ \\ x-268=0.07*15=1.05 \\ \\ x\text{ }=268+1.05=269.05 \end{gathered}`

The length of pregnancy that separates premature babies from those who are not premature is approximately 269