Question

Recall that X, the length of time to complete a pregnancy with triplets has a normal distribution with μ=231 days and standard deviation σ=9 days Because for many women it can be very uncomfortable to be pregnant with triplets too far beyond the due date, the hospital would like to induce labor with medication after some amount of time has elapsed. In order to ensure that very few women who would go into labor naturally will have to be induced, it is decided to choose an amount of time so that 95% of women will be allowed to go into labor naturally. Determine the amount of time that should be allowed before inducing a woman pregnant with triplets. This problem asks us to find the gestation time x that satisfies which of the following?

P(XP(X​
Unable to determine What is the z-score of the value x that satisfies: P(X
.9495
.8289
−1.64
−1.31
1.64
​
What is the actual gestation time x ? In other words, how many days (rounded up to the nearest day) is a woman pregnant with triplets allowed before being induced?
246 days
387.84
216.24
​

Answer 1

To determine the amount of time that should be allowed before inducing a woman pregnant with triplets, we need to find the gestation time x that satisfies P(X<x)=0.95. The actual gestation time x is 246 days (rounded up to the nearest day).

Step-by-step explanation:

To determine the amount of time that should be allowed before inducing a woman pregnant with triplets, we need to find the gestation time x that satisfies P(X<x)=0.95.

Since we know that the length of time to complete a pregnancy with triplets follows a normal distribution with mean μ=231 days and standard deviation σ=9 days, we can use the z-score formula to find the z-score that corresponds to a cumulative probability of 0.95: z = invNorm(0.95) = 1.645.

Now we can use the z-score formula to find the actual gestation time x: x = μ + zσ = 231 + 1.645 * 9 = 246 days (rounded up to the nearest day).