Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean 217 days and the standard deviation 12 days.
(a) What is the probability that a randomly selected pregnancy lasts less than 213 days?
The probability that a randomly selected pregnancy lasts less than
213 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.)
A. If 100 pregnant individuals were selected independently from this population, we would expect nothing pregnancies to last exactly 213 days.
B. If 100 pregnant individuals were selected independently from this population, we would expect nothing pregnancies to last less than 213 days.
C. If 100 pregnant individuals were selected independently from this population, we would expect nothing pregnancies to last more than 213 days.
(b) Suppose a random sample of 21 pregnancies is obtained. Describe the sampling distribution of the sample mean length of pregnancies.
(c) What is the probability that a random sample of 21 pregnancies has a mean gestation period of 213 days or less?
The probability that the mean of a random sample of 21 pregnancies is less than 213 days is approximately ?
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= 21 pregnancies were obtained from this population, we would expect sample(s) to have a sample mean of 213 days or more.
B. If 100 independent random samples of size n=21 pregnancies were obtained from this population, we would expect sample(s) to have a sample mean of 213 days or less.
C. If 100 independent random samples of size n= 21 pregnancies were obtained from this population, we would expect sample(s) to have a sample mean of exactly 213 days.
(d) What is the probability that a random sample of 62 pregnancies has a mean gestation period of 213 days or less?
The probability that the mean of a random sample of 62 pregnancies is less than 213 days is approximately ?
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= 62 pregnancies were obtained from this population, we would expect sample(s) to have a sample mean of 213 days or less.
B.If 100 independent random samples of size n=62 pregnancies were obtained from this population, we would expect
sample(s) to have a sample mean of exactly 213 days.
C. If 100 independent random samples of size n= 62 pregnancies were obtained from this population, we would expect
sample(s) to have a sample mean of 213 days or more.
(e) What might you conclude if a random sample of 62 pregnancies resulted in a mean gestation period of 213 days or less?
Answer)
As the population is normally distributed, we can use standard normal z table to estimate the probability.
Given, mean = 217
S.d = 12
Z = (x-mean)/s.d
A)
P(x<213)
Z = (213-217)/12
Z = -0.33
From z table,
P(z<-0.33) = 0.3707
If 100 pregnant individuals are selected independently from this population, we would expect 37.07 pregnancies to last less than 213 days
B)
In case of sample
Z = (x-mean)/(s.d/√n)
Z = (213-217)/(12/√21)
Z = -1.53
From z table, p(z<-1.53) = 0.0630
If 100 independent samples of size 21 are selected we would expect the 6.3 samples to have a sample mean less than 213
Get Answers For Free
Most questions answered within 1 hours.