of human pregnancies from conception to birth varies according to a distribution ately Normal with mean 266 days and standard deviation 16 days. Choose two es independently and at random. is the expected difference in the lengths of the two pregnancies? is the standard deviation of the difference in the lengths of the two pregnancies?

Calculate Expected Difference: Calculate the expected difference in the lengths of the two pregnancies. Since we are dealing with a normal distribution with a mean of 266 days, the expected value (mean) of the difference between any two pregnancies chosen at random would be 0. This is because the expected value of the difference between two identical distributions is 0. Calculation: 266 - 266 = 0Calculate Standard Deviation: Calculate the standard deviation of the difference in the lengths of the two pregnancies. The standard deviation of the difference between two independent variables is the square root of the sum of the variances of these variables. Since both pregnancies are independent and have the same standard deviation, the variance for each is the square of the standard deviation (16 days). Calculation: Variance for each pregnancy = 16^2 = 256 Sum of variances = 256 + 256 = 512 Standard deviation of the difference = sqrt(512) = sqrt(2 * 256) = sqrt(2) * 16Finalize Standard Deviation: Finalize the standard deviation of the difference. Calculation: Standard deviation of the difference = sqrt(2) * 16 ≈ 1.414 * 16 ≈ 22.624 days

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

The duration of human pregnancies from conception to birth varies according to a distribution approximately Normal with mean $266$ days and standard deviation $16$ days. Choose two pregnancies independently and at random. $\newline$ What is the expected difference in the lengths of the two pregnancies? $\newline$ What is the standard deviation of the difference in the lengths of the two pregnancies?

View step-by-step help

Home

Math Problems

Algebra 2

Interpret confidence intervals for population means

Full solution

Q. The duration of human pregnancies from conception to birth varies according to a distribution approximately Normal with mean

266

days and standard deviation

16

days. Choose two pregnancies independently and at random.

\newline

What is the expected difference in the lengths of the two pregnancies?

\newline

What is the standard deviation of the difference in the lengths of the two pregnancies?

Calculate Expected Difference: Calculate the expected difference in the lengths of the two pregnancies. $\newline$ Since we are dealing with a normal distribution with a mean of $266$ days, the expected value (mean) of the difference between any two pregnancies chosen at random would be $0$ . This is because the expected value of the difference between two identical distributions is $0$ . $\newline$ Calculation: $266 - 266 = 0$
Calculate Standard Deviation: Calculate the standard deviation of the difference in the lengths of the two pregnancies. $\newline$ The standard deviation of the difference between two independent variables is the square root of the sum of the variances of these variables. Since both pregnancies are independent and have the same standard deviation, the variance for each is the square of the standard deviation $16$ days). $\newline$ Calculation: Variance for each pregnancy = $16^2 = 256$ $\newline$ Sum of variances = $256 + 256 = 512$ $\newline$ Standard deviation of the difference = $\sqrt{512} = \sqrt{2 \times 256} = \sqrt{2} \times 16$
Finalize Standard Deviation: Finalize the standard deviation of the difference. $\newline$ Calculation: Standard deviation of the difference = $\sqrt{2}$ * $16$ $\approx 1.414$ * $16$ $\approx 22.624$ days