Question

the length of human pregnancies is approximately normal with mean $\mu = 266$ days and standard deviation $\sigma = 16$ days. complete parts (a) through (f)
(a) what is the probability that a randomly selected pregnancy lasts less than 261 days?
the probability that a randomly selected pregnancy lasts less than 261 days is approximately 0.3773
(round to four decimal places as needed )
interpret this probability. select the correct choice below and fill in the answer box within your choice.
(round to the nearest integer as needed.)
a. if 100 pregnant individuals were selected independently from this population, we would expect
pregnancies to last less than 261 days
b. if 100 pregnant individuals were selected independently from this population, we would expect
pregnancies to last exactly 261 days
c. if 100 pregnant individuals were selected independently from this population, we would expect
pregnancies to last more than 261 days

Explanation:

Step1: Understand the probability meaning

The probability \(P(X < 261)=0.3773\). This probability represents the proportion of pregnancies that last less than 261 days in the population.

Step2: Calculate the expected number

If we have \(n = 100\) pregnant individuals (a sample from the population), and the probability \(p=0.3773\) of a pregnancy lasting less than 261 days, we use the formula \(E=np\).
Substitute \(n = 100\) and \(p=0.3773\) into the formula: \(E=100\times0.3773 = 37.73\approx38\)

Answer:

A. If 100 pregnant individuals were selected independently from this population, we would expect 38 pregnancies to last less than 261 days.