Question

Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean μ=283 days and σ=17 days.

​(a) What is the probability that a randomly selected pregnancy lasts less than 277 ​days?

The probability that a randomly selected pregnancy lasts less than 277 days is approximately 0.3632 ​

(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 36 pregnancies to last less than 277 days. - correct answer

B. If 100 pregnant individuals were selected independently from this​ population, we would expect __?__pregnancies to last more than 277 days.

C. If 100 pregnant individuals were selected independently from this​ population, we would expect __?__pregnancies to last exactly 277 days. ​

(b) Suppose a random sample of 19 pregnancies is obtained. Describe the sampling distribution of the sample mean length of pregnancies.

The sampling distribution of x̅ is

▼ skewed right normal skewed left with μx=283 and σx=3.9001

(Round to four decimal places as​ needed.)

​(c) What is the probability that a random sample of 19 pregnancies has a mean gestation period of 277 days or​ less?

The probability that the mean of a random sample of 19 pregnancies is less than 277 days is approximately 0.0618.​

(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=19 pregnancies were obtained from this​ population, we would expect __?__sample(s) to have a sample mean of 277 days or less.

B.

If 100 independent random samples of size n=19 pregnancies were obtained from this​ population, we would expect __?__sample(s) to have a sample mean of 277 days or more.

C.

If 100 independent random samples of size n=19 pregnancies were obtained from this​ population, we would expect __?__sample(s) to have a sample mean of exactly 277 days.

Answer 1

answer)

A)
Mean = 283 and s.d = 17
We need to find p(x<277)
For this first we need to estimate the z score
Z = (x-mean)/s.d
(277-283)/17
= -0.35
From z table, p(z<-0.35) = 0.3632
Interpretation
If 100 pregnant individuals were selected independently from this population, we would expect (36.32~36) 36 pregnancies to last less than 277 days
C)
Mean = 283
S.d = 17
Standard error due to sample = s.d/√n
N = 19
Standard error = 3.9001
Z = (x-mean)/(standard error)
Z = -1.54
From z table, p(z<-1.54) = 0.0618
Interpretation
If 100 independent random samples of size n = 19 pregnancies were obtained from this population, we would expect 6.18~ 6 samples to have sample eman of 277 days or less