Question

Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean - 123 days and standard deviation g = 13 days. Complete parts (a) through in below. (a) What is the probability that a randomly selected pregnancy lasts less than 118 days? The probability that a randomly selected pregnancy lasts less than 118 days is approximately (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.) OA. If 100 pregnant individuals were selected independently from this population, we would expect pregnancies to last less than 118 days. B. If 100 pregnant individuals were selected independently from this population, we would expect pregnancies to last exactly 118 days. OC. 1 100 pregnant individuals were selected independently from this population, we would expect pregnancies to last more than 118 days (b) Suppose a random sample of 18 pregnancies is obtained. Describe the samping distribution of the sample mean length of pregnancies, The sampling distribution of is with w-ando- (Round to four decimal places as needed) (e) What is the probability that a random sample of 18 pregnancies has a mean gestation period of 118 days or less? The probability that the mean of a random sample of 18 pregnancies is less than 118 days is approximately (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.) OA. 100 independent random samples of size n = 18 pregnancies were obtained from this population, we would expect sample(s) to have a sample mean of 118 days or more B. I 100 independent random samples of size n-18 pregnancies were obtained from this population, we would expect sample(s) to have a sample mean of exactly 118 days. OC. 1 100 independent random samples of size n - 18 pregnancies were cbtained from this population, we would expect sample(s) to have a sample mean of 118 days or less. (d) What is the probability that a random sample of 47 pregnancies has a mean gestation period of 118 days or less? The probability that the mean of a random sample of 47 pregnancies is less than 118 days is approximately (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.) O A. if 100 independent random samples of size n = 47 pregnancies were obtained from this population, we would expect sample(s) to have a sample mean of 118 days or less B. If 100 independent random samples of size n 47 pregnancies were obtained from this population, we would expect sample(s) to have a sample mean of exactly 118 days OC. f 100 independent random samples of size n = 47 pregnancies were cktained from this population, we would expect sample(s) to have a sample mean of 118 days or more () What might you conclude if a random sample of 47 pregnancies resulted in a mean gestation period of 118 days or less? This result would be so the sample likely came from a population whose mean gestation period is In What is the probability a random sample of size 15 will have a mean gestation period within a days of the mean? The probability that a random sample of size 15 will have a mean gestation period within 8 days of the mean is (Round to four decimal places as needed.) 123 days

Answer 1

Note : Allowed to solve only 4 questions per post.

a. Probability that a randomly selected pregancy lasts less than 118 days

We are given mean = p= 123 standard deviation = 0 = 13 X = 118 We need to find P(X<118) First we find the Zscore Zscore X-() 118-(123) =-0.3846 13 Using the normal distribution table we find pvalue P(X<118) = 0.3503 Hence the needed probability P(X<118) = 0.3503

Correct option A: If 100 pregnant individals were selected independently from the population we would expect 35 pregnancies to last less than 118 days.

b. Sampling distribution of mean length of pregnancies

The sampling distribution of 7 is Normal Jy = 123 13 0 3.064129 n V18

c. We use t distribution in this case since the sample size is less than 30

Probability less than a value* We are given Sample mean = p= 123 Sample standard deviation = 0 = 13 X = 118 n =18 We need to find P(X<118) First we find the tscore X-4 tscore =-1.6318 118-123 13 VIS 15 Using the students distribution table, we find pvalue with df = 18-1 = 17 P(X <118) = 0.0606 Hence the needed probability P(X <118) = 0.0606

Correct option : C: if 100 independent random samples of size n = 18 pregancies were obtained from the population, we would expect 1 sample to have a sample mean of 118 days or less.

d. In this case we can use normal distribution as the sample size is greater than 30

We are given Population mean = u= 123 standard deviation = 0 = 13 X = 118 n =47 We need to find P(X<118) First we find the score Zscore = * =-2.6368 118-123 13 15 Using the normal distribution table we find pvalue P(X <118) = 0.0042 Hence the needed probability P(X <118) = 0.0042

probability is about 0.0042

Correct option :
A:if 100 independent random samples of size n = 47 pregancies were obtained from the population, we would expect 0 sample to have a sample mean of 118 days or less.