Question

the length of human pregnancies is approximately normal with mean μ = 266 days and standard deviation σ = 16 days. complete parts (a) through (f)
click here to view the standard normal distribution table (page 1). click here to view the standard normal distribution table (page 2).

the probability that the mean of a random sample of 7 pregnancies is less than 260 days is 0.1611
(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 independent random samples of size n = 7 pregnancies were obtained from this population, we would expect \\(\square\\) sample(s) to have a sample mean of 260 days or less.
b. if 100 independent random samples of size n = 7 pregnancies were obtained from this population, we would expect \\(\square\\) sample(s) to have a sample mean of exactly 260 days.
c. if 100 independent random samples of size n = 7 pregnancies were obtained from this population, we would expect \\(\square\\) sample(s) to have a sample mean of 260 days or more.

Explanation:

Step1: Identify the formula

To find the expected number of samples, we use the formula: Expected number = Probability × Number of samples.
Here, the probability is 0.1611 and the number of samples is 100.

Step2: Calculate the expected number

Multiply the probability by the number of samples: \( 0.1611 \times 100 = 16.11 \).
Since we need to round to the nearest integer, we get 16.

Answer:

16