Question
The length of human pregnancies is approximately normal with mean
parts (a) through (f).
Anterpret this probability. Select the correct choice below and fill in the answer box within your choice.
(Round to the nearest integer as needed.)
B. If 100 pregnant individuals were selected independently from this population, we would expect
than 258 days.
C. If 100 pregnant individuals were selected independently from this population, we would expect
exactly 258 days.
parts (a) through (f).
Anterpret this probability. Select the correct choice below and fill in the answer box within your choice.
(Round to the nearest integer as needed.)
B. If 100 pregnant individuals were selected independently from this population, we would expect
than 258 days.
C. If 100 pregnant individuals were selected independently from this population, we would expect
exactly 258 days.
Ask by Garrett Love. in the United States
Dec 02,2024
Upstudy AI Solution
Tutor-Verified Answer
Answer
B. 31
C. 0
C. 0
Solution
To solve parts (B) and ©, we will use the properties of the normal distribution.
Part B: Expectation of Pregnancies Lasting Less Than 258 Days
-
Calculate the Z-score for 258 days:
-
Find the probability of a pregnancy lasting less than 258 days:
Using the Z-table or a standard normal distribution calculator, we find the probability corresponding to. The probabilityis approximately . -
Calculate the expected number of pregnancies lasting less than 258 days:
If 100 pregnant individuals are selected, the expected number is:Rounding to the nearest integer, we expect approximately 31 pregnancies to last less than 258 days.
Part C: Expectation of Pregnancies Lasting Exactly 258 Days
In a continuous distribution like the normal distribution, the probability of any single exact value (like exactly 258 days) is technically 0. Therefore, we would expect:
Summary of Answers:
- B: If 100 pregnant individuals were selected independently from this population, we would expect 31 pregnancies to last less than 258 days.
- C: If 100 pregnant individuals were selected independently from this population, we would expect 0 pregnancies to last exactly 258 days.
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Extra Insights
In the world of statistics, when we deal with normally distributed data—like the length of human pregnancies—it’s fun to visualize it as a bell curve! The 266-day mean represents the peak of this curve, while the standard deviation of 16 days reveals how spread out the data points are. To find the probability of a pregnancy lasting less than 258 days, we can use the z-score formula to compare it against the expected distribution, giving us the desired insights about our sample.
When calculating the expected number of pregnancies lasting less than 258 days for a sample of 100, we would use the cumulative probability corresponding to the z-score derived from the mean and standard deviation. However, it’s crucial to note that the probability of a single day (like exactly 258) occurring in a continuous distribution is technically zero. Thus, we wouldn’t expect to find any pregnancies lasting exactly 258 days; rather, we look for a range, making it a delightful topic where mathematics meets real-life experiences!
