the length of human pregnancies is approximately normal with mean $ \mu = 266 $ days and standard deviation $ \sigma = 16 $ days. complete parts (a) through (f).

b. if 100 independent random samples of size $ n = 38 $ pregnancies were obtained from this population, we would expect sample(s) to have a sample mean of exactly 261 days
c. if 100 independent random samples of size $ n = 38 $ pregnancies were obtained from this population, we would expect 3 sample(s) to have a sample mean of 261 days or less
(d) what is the probability that a random sample of 61 pregnancies has a mean gestation period of 261 days or less?
the probability that the mean of a random sample of 61 pregnancies is less than 261 days is approximately 0.0073
(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 = 61 $ pregnancies were obtained from this population, we would expect sample(s) to have a sample mean of exactly 261 days.
b. if 100 independent random samples of size $ n = 61 $ pregnancies were obtained from this population, we would expect sample(s) to have a sample mean of 261 days or more.
c. if 100 independent random samples of size $ n = 61 $ pregnancies were obtained from this population, we would expect sample(s) to have a sample mean of 261 days or less

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).

b. if 100 independent random samples of size $ n = 38 $ pregnancies were obtained from this population, we would expect sample(s) to have a sample mean of exactly 261 days
c. if 100 independent random samples of size $ n = 38 $ pregnancies were obtained from this population, we would expect 3 sample(s) to have a sample mean of 261 days or less
(d) what is the probability that a random sample of 61 pregnancies has a mean gestation period of 261 days or less?
the probability that the mean of a random sample of 61 pregnancies is less than 261 days is approximately 0.0073
(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 = 61 $ pregnancies were obtained from this population, we would expect sample(s) to have a sample mean of exactly 261 days.
b. if 100 independent random samples of size $ n = 61 $ pregnancies were obtained from this population, we would expect sample(s) to have a sample mean of 261 days or more.
c. if 100 independent random samples of size $ n = 61 $ pregnancies were obtained from this population, we would expect sample(s) to have a sample mean of 261 days or less

Accepted Answer

# Explanation:
## Step1: Calculate the expected number of samples
The probability that the mean of a random sample of $n = 61$ pregnancies is less than $261$ days is $P\approx0.0073$.
If we have $N = 100$ independent random samples, the expected number of samples with a sample mean of $261$ days or less is $E=N\times P$.
Substitute $N = 100$ and $P=0.0073$ into the formula: $E = 100\times0.0073$.
## Step2: Round the result
$E=0.73\approx1$ (rounded to the nearest integer).

# Answer:
C. If 100 independent random samples of size $n = 61$ pregnancies were obtained from this population, we would expect $1$ sample(s) to have a sample mean of 261 days or less.

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QUESTION IMAGE

Question

Explanation:

Step1: Calculate the expected number of samples

Step2: Round the result

Answer: