Answer:
1) 3.67%
2) 60.39%
3) The longest 20% of pregnancies last at least 277 days.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
Question 1. What percent of pregnancies last less than 240 days?
This is the pvalue of Z when X = 240. So
has a pvalue of 0.0367
3.67% of pregnancies last less than 240 days
Question 2. What percent of pregnancies last between 240 and 270 days?
This is the pvalue of Z when X = 270 subtracted by the pvalue of Z when X = 240. So
X = 270
has a pvalue of 0.6406
X = 240
has a pvalue of 0.0367
0.6406 - 0.0367 = 0.6039
60.39% of pregnancies last between 240 and 270 days
3. The longest 20% of pregnancies last at least how many days?
They last at least X days, in which X is found when Z has a pvalue of 1-0.2 = 0.8. So it is X when Z = 0.84.
The longest 20% of pregnancies last at least 277 days.